astap.png ASTAP, the Astrometric STAcking Program    ASTAP Forum        Documentation     Version history   Checklist for solving   
             astrometric (plate) solver, stacking of images, photometry and FITS viewer

Download installers:
Operating systemProgram installerLarge star databaseSmaller star database Photometry & colour star databaseLarge galaxy database
Window 64 bitProgram (0.9.584, dated 2021-10-8) or α versionH18H17V17Hyperleda
Window 32 bitProgram zipped (0.9.584)
Linux 64 bitProgram debian (0.9.584),
Program .tar.gz
openSUSE and Fedora support
α version
H18H17V17Hyperleda


Linux 32 bitProgram (0.9.570)
Raspberry PI, 32 bitProgram (0.9.570)
Raspberry PI, 64 bitProgram (0.9.570)
MacOS 64 bitProgram (0.9.584a)

Program executable for M1 zipped
(ß version 0.9.584a, code signing required. Significant faster.)
H18H17V17included with star database

You have to install:
1) Program
2) One star database.

You will need only one database, either the H18 (980 mbyte) or the H17 (500 mbyte). The H18 will work in all cases but if your field of view (image height) is larger then one degrees you could use the smaller H17 . If you have both the H17 and H18 installed then delete the H17 or select the correct database in tab alignment. The V17 is only required for photometry. Older G17 and G18 star databases are 
obsolete can be uninstalled/deleted.

Star database usability:


For comment feedback and questions there is the ASTAP Forum. The ASTAP Manual is below

For photometry you could download and install the V17 star database colour up to magnitude 17. A 680 MB file. It contains the calculated Johnson-V magnitude and colour information (GBp-GRp) for star annotations. This one also works best for solving an image with a FOV of more then ten degrees

Hyperleda, a very large galaxy database for deep sky annotation. 2.190.000 objects. Based on extract from leda.univ-lyon1.fr/  Will be placed in the program directory.


Alternative links & development version:
Operating systemProgram development versionAlternative star database links
Fits image compression & decompression programs from Nasa HEASARC.  Only required if you have files with the .fz  extension.Barebone command-line solver compatible with the GUI version if renamed. No pop-up notifier. Will not accept raw files and will not work with SharpCap since FOV is not stored.
Window 64 bitASTAP_installer_(0.9.585, 2021-10-15),
ASTAP executable only
H18 installer
H17 installer,
G17 installer (obsolete 1)).

H18 zipped,
H17 zipped,
G18 rar ((obsolete 1)),
for manual install at  \programs files\astap or program directory

Fpack & Funpackastap_cli (v0.9.580
Window 32 bitastap_cli (v0.9.580)
Linux 64 bitASTAP_debian_package_(0.9.584), 
ASTAP tar.gz
H18 debian
H17 debian
G18 debian.

H18 zipped
H17 zipped
V17 zipped , 
G18 as rar ((obsolete 1)),
G17 zipped ((obsolete 1))
for manual install at /opt/astap


install from distributionastap_cli  (v0.9.580)
Linux 32 bit
Raspberry PI, 32 bitastap_cli  (v0.9.570)
Raspberry PI, 64 bitastap_cli  (v0.9.570)
MacOS 64 bit
H18 zipped
H17 zipped
V17 zipped , 
for manual install at  /usr/local/opt/astap
astap_cli (v0.9.580)
Mac M1Program executable for M1 zipped
(ß version 0.9.584a, code signing required)


  Donations are welcome:



  Documentation, contents:




ASTAP introduction

ASTAP is a free stacking and astrometric solver (plate solver) program for deep sky images. In works with astronomical images in the FITS format, but can import RAW DSLR images or XISF, PGM, PPM, TIF, PNG and JPG  images. It has a powerful FITS viewer and the native astrometric solver can be used  by CCDCiel, NINA, APT or SGP imaging programs to synchronise the mount based on an image taken.

Main features:
  1. Native astrometric solver, command line compatible with PlateSolve2.
  2. Stacking astronomical images including dark frame and flat field correction. 
    • Filtering of deep sky images based on HFD value and average value.
    • Alignment using an internal star match routine,  internal astrometric solver.
    • Mosaic building covering large areas using the astrometric linear solution WCS or WCS+SIP polynomial. 
    • Background equalizing.
  3. FITS viewer with swipe functionality, deep sky and star annotation, photometry and CCD inspector.
    • FITS thumbnail viewer.
    • Results can be saved to 16 bit or float (-32) FITS files.
    • Export to  JPEG, PNG, TIFF, PFM, PPM, PGM  files.
    • FITS header edit.
    • FITS crop function.
    • Automatic photometry calibration against Gaia database, Johnson -V or Gaia Bm
    • CCD inspector
    • Deepsky and Hyperleda annotation
    • Solar object annotation using MPC ephemerides
    • Read/writes FITS binary and reads ASCII tables.
  4. Some pixel math functions and digital development process
  5. Can display images and tables from a multi-extension FITS.
  6. Blink routine.
  7. Photometry routine
  8. Available for MS-Windows 32 & 64 bit,  Linux 32, 64 bit, MacOS 64 bit, Raspberry-Pi Linux 32 and 64 bit.

Stacking of images:

Stacking of astronomical images is done to achieve a greater signal to noise ratio, prevent sensor saturation and correct the images for dark current and flat field. Additional imperfect images due to guiding, focus  problems or clouds can be removed.

This is a screen short of the stack menu. It contains several tabs for the file list and settings. File can be sorted on quality and values.The image can be visually inspected in the viewer by a double click on the file or using the pop-up menu.



Program requires FITS images or RAW files as input for stacking, but it can also view 16 bit PGM /PPM files, XISF files or  in 8 bit  PNG, TIFF or BMP files. For importing DSLR raw images  the program
DCRAW from David Coffin or LibRaw is used.
For stacking the internal routine compares the image star positions to align.



Astrometric Solving:


ASTAP can be
used as astrometric solver to synchronise the telescope mount position with center position of an image taken with the telescope. Existing images can be solved to annotate, for photometry or the measure positions of unknown objects.

The ASTAP solver aims at a robust star pattern recognition using the catalog star coordinates in Equinox J2000. The solution is not corrected for optical distortion, refraction, proper  motion  of  stars and other minor effects all to be very minor.

The process astrometric solving is often referred to as a "plate solve". That was a correct description in the past, but in modern times there are no photographic plates involved in the process.


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Program installation:

MS-Windows:

The installer and separate star database will be default installed at c:\Program Files\astap.  But they can be placed anywhere as long all files are in the same directory.

Linux installation:

The program and database are provided as a Debian package and will be installed at  /opt/astap. The program is also a rpm package is available.  In case the executable is manually placed at /usr/..., then the program will look for the database at /usr/share/astap/data/ (version 0.9.412b or higher)

MacOS installation:

The program and star databases are are provide as pkg file. The star database will be installed at /usr/local/opt/astap/



Program operation, stacking astronomical images:

The purpose of the stacking routine is to combine astronomical images to reduced noise and to flatten the image.

 Ideally you should have collected

Only light frames are essential.

The automatic stacking process in ASTAP goes through the following steps:
  1. The flats will be combined to an average and the combined average flat-darks will be subtracted to  have a near ideal presentation of the vignetting called the master flat frame.
  2. The darks will be combined to an average master dark.
  3. Optional on the master flat a  2x2, 3x3 or 4x4 mean filter is applied to reduce noise.
  4. From each light frame the master dark will be subtracted to extract the pure deep sky signal.
  5. Each light frame will be flattened by dividing it by the master-flat resulting in the corrected light frames.
  6. The corrected light frames are combined to the final image using the average or sigma clip mean (to remove outliers as satellite tracks) method. 
Step 3,4,5,6 are done in memory. No intermediate results are stored on disk.

It is possible to mix different exposure times but it is not recommended.


Operation of the stacking program

Start the ASTAP program.


Call up the stack menu window using the  ∑   button.

a) Select frames
In tab
images select the lights. In tab dark select the corresponding darks.  Select in tab flats the flat-field images called flats and in tab flats-darks the flat-darks/bias frames. In most cases you could select all frames in tab images. The program will move the fames to the corresponding tab during analyse. The light and dark should preferable have the same exposure time and temperature. The flats should have the same exposure time and temperature as the flat-darks.

b) Analyse and remove bad frames
I
n tab images (for the light frames), press analyse and remove manually any poor image. Poor images can be detected by a too high HFD (Half flux diamater stars), low number of stars or high background value( by clouds) .
Loss of tracking could result in too low HFD value. If required inspect each image by double on the file name. The list can be sorted by clicking on the corresponding columns. Using the pop-up menu selected bad frames can be renamed to *.bak for deletion later.

c) Set parameters in tab stack method
In tab stack method select the stacking method, average or sigma-clip-average. For OSC camera images  select "Convert OSC images to colour". Select the correct Bayer pattern (4 options). Test the required pattern first in the viewer with a single image. The source images should be raw (gray)  without colour produced by  astronomical camera's.

d) Set parameters in tab alignment
Leave this to the default star alignment.

e) Classify by
Leave all check marks 
initially unchecked. (This is an option to select automatically a master dark with the correct temperature and exposure time for the lights. Same for  master flat selection  based on filter used both in the light and flat.)

f) Press the  Stack (..) button.
The darks and flats & flat-darks will be combined in a master dark and master flat frame. Then the program will combine the light frames to the final image and save it automatically to FITS. This will take some time.

g) Export
The stack result will be saved as FITS. The program keep a record of all results in tab Results. Stretch the image as required.  Crop the sides if required using the pop-up menu. Equalise the back ground if required using the tool in tab pixel math. Export as stretched JPG or 16 bit bit stretched/unstretched  PNG / TIFF.  The stretched export follows the gamma and stretch setting of the display.  For further image processing you could export to 32 bit float TIFF or 32 bit float PFM format.

ASTAP export types:



File formats ASTAP8 bit16 bit32 bit
ImportFITS, JPEG, PNG, TIFFFITS, PNG, TIFF, PPM, PGM, raw formatsFITS, PFM
ExportFITS, JPEG, PNG, TIFFFITS, PNG, TIFF, PPM, PGMFITS, TIFF, PFM


  


All the program settings and file selections will be save by leaving the program or click on the  Stack check marked images   button.

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The stack menu:



Images, darks, flats can be added using the  Browse   button or can be drag dropped on the form.

For a generic description how to stack see
Program operation, stacking astronomical images

Poor images can be filtered by either 1) HFD value,  2) Quality,  3) Star-level or  4) Background value.

Stack multiple objects: Several objects can be stacked in one run. If the classify-by-object is check-marked, the program will stack all objects and save the results using the available darks and flats.

Analysing and removing of the bad ones: Before stacking the images can be analysed with the
 Analyse button. Images with a high HFD value are most likely unsharp and can be inspected in the viewer by double click on the filename. The file can be renamed to *.bak by the pop-up menu to be removed later. Images with a high background indicating clouds or twilight should be removed/renamed to *.bak.

Sorting: Images can be sorted on any of the columns. For example if you click on HFD, the images will be sorted on HFD. You could then remove the images with the highest value or inspect them by double click on the file name.

Dark classification: If classify by exposure time and/or exposure time is check-marked the program will automatically select the correct darks or master dark. So it is possible to keep several dark files check-marked in the darks tab and the correct master dark will be selected automatically.

Colour stack and Colour filter classification: If
the classify-by-filter is check-marked, the stack routine will combine the available filters to a RGB image. If only Red + Green +Blue image are available they will be combined in a RGB image. If Luminance images are available it will first stack the RGB colors and then apply a most-common-filter and Gaussian blur on the RGB result. Finally the luminance image is coloured with the RGB result. The filter factor should be set typically near 20.

For nebula you could combine RGB or LRGB. If a luminance filter is detected the LRGB mode is used. First the RGB is combined, stars are removed using a most common filter, the image is then blurred with a Gaussian blur and and the colour is then applied luminance channel. Star colour is lost with this process. The filter names can be set in tab alignment

To record star colours use RGB only.

It could be better to stack in two steps. First prepare the Red, Green, Blue and Luminance stacks. Then run a stack again with the 
Red, Green, Blue and optional Luminance. Or if you could revisit the produced interim results in the RESULTS tab en copy them to the IMAGES tab using the pop-up menu. You could try different colout factors.

Image file names containing "_stacked" will be
un-checked by default to prevent stacks by accident are re-used. If required, just select the file and check-makr it again.

Organising images, darks, flats and flat-darks: Images placed in the first tab will be organised based on the FITS header keyword
IMAGETYP. So as soon you click on the image  Analyse   button, dark and flats and flat darks/bias images will be move to the corresponding tab.

Keyword modification: The pop-up menu has option to update a keyword of multiple files if required.

OSC images (one shot colour images): To import raw files from a digital camera, ASTAP can either use  DCRAW or LibRaw for conversion. You can select it in tab "Stack method". Libraw has some advantages since the conversion program convert directly to FITS and exposure time, date of exposure and demosaic pattern are written to the FITS header.

For stacking of  OSC images it is best to start with raw images. The raw colour images look mono, but the program will convert them to colour later in the stacking process. There are four different Bayer patterns. The demosaic pattern can be set in
the tab "stack method". Try auto or empirical which will result in the correct colours. A terrestrial image could help find the correct demosaic settings. Load a raw image in the viewer and in tab "Stack method" test conversion with button "Test pattern". Try auto or the four demosaic patterns. If the colours are not correct, just hit undo button or type CTRL-Z to recover and try an other demosaic setting.

Power down option after completion:  If stacking takes a long time you could activate this option and the program will be power-down the computer after completion.

  Clear  , button to remove all files from the list.

   ||        , button to stop blinking cycle.

    >>    , starts a continuous un-aligned blinking cycle. This is intended to find visually outlier images where guiding has briefly failed.



How to exclude poor images

Sort the images on quality by double clicking on the column quality
and inspect visually the images with the lowest quality factor by double click on the row. If poor, rename images with right mouse button popup menu "rename to *.bak" for deletion later.  Sort also on background and inspect visually the images with too high values on possible cloud coverage or twilight conditions by double click on the row to open.

To uncheck/untick poor images can als be done automatically. First check mark the option "After analyse untick worst images". Then press button  Analyse and organise images  . The column quality of the images will be analysed statistacally and outliers can be removed using either a  standard deviation  represented by the Greek lower case sigma σ letter or a percentage. 

For a normal distribution you could expect the following:

Confidence interval Proportion within
1σ 68%
1.5σ 87%
2σ 95 %
2.5σ 98.8%
3σ 99.7%



Satellite tracks

The stack method
"sigma clip average" should normally remove any satellite tracks. If after stacking with "sigma clip average" there are still satellite tracks visible, you could lower in tab "Stack Method". the sigma factor from 2.5 to a lower value maybe 2.2 . An other way is the blink/scroll  through the images with the   >>   button. As soon you see an abnormal bright track on the image stop the blinking by esc and inspect visually the image(s)  involved by double click on the row. Remove any poor image by using right mouse button popup menu "rename to *.bak"



Results tab.

The stack results are reported in the results tab. By a double click they can be viewed the viewer. The number of files and exposure times are given. With the pop-up menu it is possible to copy the image file path to the clipboard for use in a file explorer.
 


Back to index


Stack method tab


The best stack option is "Sigma clip average". For only 2 or 3 images or when you are in a hurry or for testing "average"will do.
    
Stack methodStackingDescription
Average StackingFor fast stacking. Satellite tracks will not be removed.
Sigma clip averageStacking, satellite tracks will be removed. Reduce the σ factor for more aggressive filtering of the satellite tracks.
Astrometric image stitching modeMosaicThis will stitch astrometric tiles. Prior to this stack the images to tiles and check for clean edges. If not use the "Crop each image function". For flat background apply artificial flat in tab pixel math 1 in advance if required.  Adapt the mosaic canvas height and width if required, default is 2.
Calibration and alignment of the files onlyDarks and flats will be applied. The images will be aligned to the reference image.
Calibration of the files onlyDarks and flats will be applied.
Average stacking, skip LRGB  combineSatellite tracks will not be removed. Stacks based on filter will not be combined to RGB.
Sigma clip average, skip LRGB combineSatellite tracks will be removed. Reduce the σ factor for more aggressive filtering of satellite tracks. Stacks based on filter will not be combined to RGB.



Raw one shot colour images (OSC):
 
RAW images of  DSLR cameras /One shot color cameras are monochrome and have to be converted into colour images (after applying darks and flats). This converson is called demosaic or debayer. First set Bayer pattern correctly by loading a raw image (grayscale) in the viewer and try one of the bayer patterns till the image colours match in viewer. If not hit CNTRL-Z to undo and try a different Bayer pattern.

There are several methods to convert (demosaic/debayer ) the raw image  to colour:
  • AstroC, colour for saturated stars, as bilinear method but for saturated stars the program tries reconstruct the star colour. Select the range which matches with the value of brightest stars.
  • AstroM, white stars, as bilinear method but if there is an unbalance between the 4 red, 4 blue or 2 green pixels it uses luminance only. Effective for unsampled images and stacks of a few images only. Star colour is lossed if undersampled but star will become white.
  • AstroSimple ©, each R,G, G, B pixel colour information is used in a 2x2 pixel range. Simple but very effective for astro images. Works best for a little oversampled images. Stars have very few artifact if any. 
  • Malvar-He-Cutler 1), advanced method for interpolation developed for terrestial images but less suitable for OSC astro images. The background noise is lower.
     Creative Commons License AstroSimple is © Han Kleijn, www.hnsky.org, 2020. and licensed under a Creative Commons Attribution 4.0 International License.
 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.                       
What to select:

The principle of the AstroSimple demosaic method:

The ASTAP demosaic method Simple

Auto levels:  This is an option to white balance the final colour result. The stars will be average white and the background sky will be gray.

Normalise OSC flat:  This option should normally be switched off. Only if your light source for making the flats was very reddish or blueish, you could this option equalise the red, green and blue level. Binning is not recommended for flats since individual sensitive  differences between pixels are compensated by the flat.


Colour smooth:  This is an option to smooth the de-mosaic artifacts. The colour is smoothed while preserving the luminance signal.



The background colour noise can be removed with option "Background colour removal" in the pixel math tab of the stacking menu.

The DSLR OSC images will be automatic converted to FITS files.



Oversize:
This is default set at zero but could be set hunderd pixel or larger. This overlap was introduced to show partly overlapping images. If you don't want a black area around the image set this value to zero.

If your using a monochrome filter like H-alpha with a DSLR/OSC sensro, use the viewer Tool menu to split the images in R, G, G, B before stacking and use the R=red image for future processing.

The program settings will be saved automatically if your either exit the program or start a stack.



Image stiching method (Mosaic)

Astrometric image stiching is possible with the internal astrometric solver. The reference of each pixel is the astronomical position. So stacking is not done against a reference image but against an position array set by the first image.  You have to set the in tab alignment the settings for "Image stiching (method)" correctly. If you stitch 4 images, you have set "Mosaic width/height  in tiles:" at 2. This will provide enough space to place for the 2x2 mosaic.

Here a suggested work method:
  1. Stack the tiles separately using method "SIGMA-CLIP-average" and use for the alignment the internal STAR alignment method.  Inspect the resulting tiles and crop them if required. You can also crop them later automatically with "Mosaic skip outside pixels" Do this for each color separately if you have separate files.
  2. In tab  "stack method" select option "IMAGE STICHING METHOD" and select astrometic alignment using either the internal solver.
  3. In tab "stack method", set the "mosaic width/height" correct and check-mark the option "equalise background".  If the input images have poor borders, set option crop images larger then 0%.
  4. Select the files. Most likely the files names contain "_stacked, so you have the check-mark the files after selection.
  5. Click on the button   Stack check marked images|  
  6. Crop the stacked result using the image crop option in the viewer mouse pop-up menu.
  7. Adjusted the stretch range and save as JPEG, 90% quality.
Here an example mosaic x 4 of M31 made with ASTAP:





Here an example of a mosaic build of DSS images:

The size can be reduced by a crop function (right mouse button) later. Making the oversize too large could result in memory overload.



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The alignment menu tab:

For alignment there are four options, internal star alignment,  native astrometric solver, manual alignment or ephemeris alignment. For mosaic building you have to use the internal astrometric solver.


 Internal star alignment



This internal star matching alignment is the best and fastest option to stack images. It is not suitable for mosaics. No settings, fully automatics alignment for shift in x, y, flipped or any rotation using the stars in the image. It will work for images of different size/camera's with some limitations.

The program combines four close stars into an irregular 2D tetrahedron or kite like figure (and compares the six irregular tetrahedron dimensions with irregular tetrahedrons of the first/reference image. It selects at least the six best matches and uses the centre position of the irregular tetrahedrons in a least square fitting routine for alignment.  The four stars are called a quad. The six distances are used to construct a hash code.

There is only two settings relevant but normally you don't have to change them.

The following image shows the selected quads where the six distances form an irregular tetrahedrons :


The matching process is described here
Background info, how does the ASTAP astrometric solving works internally


Astrometric alignment.

   Internal astrometric solver (plate solver). The works with the same four star quad as for the Star alignment option. The quads are compared with the G17 star database (to be installed in the program directory). It has the following settings:

The internal plate solver works best with raw unstretched and sharp images of sufficient resolution where stars can be very faint. Exposures 5 to 300 seconds. Heavily stretched or photo shopped images are problematic. 

For those are interested:  
Background info, how does the ASTAP astrometric solving works internally




Manual alignment.

Manual alignment

This option allows alignment of the images based on a single star, asteroid or comet. If this option is activated, the list of images in the image tab turns red. Double click on each image in the list and click on the star/comet of asteroid to be used as reference. This object is then marked with a little purple circle. The position will be auto centered. (and the X,Y position will be added to the list) A poor lock is indicated by a square. If so try again till it is a circle. If all images in the list are turned green, so contain a value, then click on the 
  Stack button  .

Options:
  • Star centering
  • Comet centering
  • No alignment


For objects which are moving in the sky, select the stack option "average" and not option "sigma clip".



Ephemeris alignment

Rather then manual selecting the center point it is also possible to use the ephemeris of an asteroid or comet. In ASTAP this is reallised by using the annotation markers written in the header. 


To align go through the follow steps:

Preperation:   
Stacking:

Only the object selected will be sharp. The stars will form trails


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Blink tab

This tab allows to blink images and to measure variable stars. 

Blink comparator

This option allows rapidly cycle (blinking) through the images taken of the same area of the sky at different times. This will allow the user to spot easier moving objects.  While blinking the result can be demosaiced (slow) if the "auto demosaic" option in the viewer is activated.

     ||      , button stops the blink cycle.  

     >      , button starts one blink cycle.

     >>   , starts a continuous blink cycle.

☑ Align images. With this option check-marked,the images will be aligned using star alignment.  The alignment will be refreshed after pressing "clear alignment"

☑ Time stamp. With this option a time stamp from the header will be written to the bottom of the image. If the displayed image is saved as FITS, this time stamp will be written to the saved image. 

☑ Filter out stars based on first image,  With this option check-marked,the stars will covered with a black circle allowing easier to spot moving objects.. The black cover size can be increased with option "star suppression diameter".  The star detection can be optimised with the  factor".

  Clear, button to remove all files from the list.

Export video   This button will export the blink result to an uncompressed .y4m video file (YUV4MPEG2). For OSC images, activate in the viewer  the "auto demosaic" option. The menu will ask for a video file name and desired frame rates per seconds. Contrast will be as set in viewer. Compression can be achieved in an external program like VLC or leave it to YouTube.  If time-stamp is check marked then the time stamp will be written to the video.

Export aligned This button allow the creation of aligned FITS images. If  blinking with alignment works well, stop blinking and hit this button  All images will be copied aligned to new files ending _aligned.fit. Alignment will be done against the first image in the list. If time-stamp is check marked then the time stamp will be written to the aligned images.


Photometry tab

This tab allows measuring the magnitude change of one object in a series of images and detects automatically the four most variable objects.  The butttons work the same as in the blink tab.

Select the images to analyse. Click on one of the      >       buttons to cycle trough the images  The program will do the following:

  1. Cycle 1, Find an astrometric solution for all selected images and write the solution to the FITS file header. 
  2. Cycle 2. In a second cycle, the program will identify stars in the image and measure the star flux against the V17 star database. The mean flux/magnitude factor exlcuding outliers will be used later to measure the magnitude of any object in the image series. So prior to this install and use the V17,  Johnson-V version of the star Gaia database provided.
  3. At the end of cycle 2, it will mark the four most variable stars with a yellow circle.
  4. Click on up to three stars. Violet circles labeled Var, Check and 3 will mark the stars. If you click twice on a stars the labels will rotate between the stars. The measured magnitudes of each image will be written to the file list. This complete list can be exported to a spreadsheet using the pop-up menu allowing the creation a magnitude curve over time.
  5. With   AAVSO   button an extended report can be generated.  As comparison star always the Gaia stars are used, so select in ASTAP only the V17 database. You have to enter the designation of the Variable and Check star. The report format is according the AAVSO Extended file format.

For maximum accuracy it is better to first to calibrate the images with darks,  flats & flat darks. This can be done using  the "calibration only"option in tab "stack method" and then executing the regular stack procedure.

Note that the measured star flux is compared and calibrated with the star database. For most cases you should install the V17 star database containing the Johnson-V magnitudes. After stopping the cycle it is possible to measure any object using the mouse pointer.

Note: ASTAP uses for calibration  up to 1000 stars from the Gaia database.  So all stars it can find and recognise  in the image with an  SNR>30.  So the Gaia database should be the V17 which contains the calculated Johnson-V magnitudes. The three stars are just measured against the Gaia Johnson-V database. Only two are required for the report. The you just need to select the variable star and a check star. The third star (3) is just a bonus.

From the up to 1000 calibration stars any outlier star is removed if it deviates more then 1.5 sigma from the median factor (Gaia_star_magn - log(flux). For the remaining stars the factors are averaged and used for flux calibration of the variable and check star.. So it is a different setup then usual but there is never lack of calibration stars.

Alignment of the images is done using the astrometric (plate) solution. The astrometric solution is written to the orginal file header. You can refresh the photometric and astrometric calibration using the dedicated buttons for this.

The list contains three dates:
To convert the Julian Day to a date and time in the spreadsheet, subtract the Julian Day by -2415018.5 and format as date or time.

For a series of images, the standard deviation of the measured star magnitudes is typical better then 0.02 magnitudes. The standard deviation of the Check star is used for error estimate if more then 4 images are selected. else an estimate based on the Variable SNR values is used. The star flux values should be below saturation (65500)  but reasonable high.

Note that it is beneficial to de-focus an image a little to prevent pixel saturation and spread the flux measurement over more pixels. It also allows longer exposure times. However the image should reasonable focused to allow solving.


Preparation and usage of DSLR images for photometric measurements:

Step 1) and 3) are DSLR camera specific.

  1. Define Bayer pattern: The green pixels of a DSLR camera have a very similar response as a Johnson-V filter and can be reported as filter TG. So to use the green pixels only, it is required to extract the green pixels from the raw. The images should NOT be converted to colour by the de-mosaic routine. To allow to extract the green pixel it is required to define the correct de-mosaic pattern in ASTAP. Load a raw image in ASTAP and in tab "Stack method" check-mark temporary option "convert OSC images to colour". Set Bayer pattern to Auto or one of the other patterns and test the conversion to colour with button "Test pattern". This is best done with a terestial image to be sure. If the correct pattern is select and the colour produced are correct then unselect the option "convert OSC images to colour".
  2. Calibrate: For maximum accuracy it is better to calibrate the images with darks and flats & flat-darks. Select in tab "Stack method" for the stack method option  "calibrate".  Do not use "calibrate &alignment"and uncheck option  "convert OSC image to colour". Load the images in the light tab, darks in the dark tab, flats in the flat tab and  flat-darks in the flat-darks tab. Press the large button "Stack.". New calibrated image will be created ending with "_cal.fit".  If no darks and flat are available, proceed without calibration.
  3. Extract green (or red, blue) pixels.  Load the new images in the photometry tab. Press the button "extract RGB extraction" and select green. Images will be converted to new images with filename ending "_cal_TG.fit".
  4. V17. Check if V17 star database is selected in tab "Alignment". if it is not available download the V17 and select it.
  5. Astrometric solutions . If the images are not solved yet, press button "Refresh astrometric solutions" This is required to identify the stars for photometric calibration against the V17 star database. If no solution are found, check the image "Field of view (height)" in degrees in tab "alignment" and check initial α,δ
    δ
    δ
    δ
    δ
    δ
    δ del
     positon in the viewer. If solving fails, got through the check list for solving.
  6. Mark the Var star and Check star.  Double click on the first image in the list and select the Var and Check Star and star 3. If you click a second time on a star the three stars will be swapped.  Star 3 is not required for reporting, just an extra star.
  7. Cycle. Press the       >|       button and check if the magnitudes are recorded. Check if stars are still proper selected. To indentify stars you could select Ännotate variables". The database should be complete up to magnitude 12 .
  8. Aperture, adapt aperture and annulus for maximum accuracy.  Use for this the reported standard deviation of the check star in the log.
  9. AAVSO.  Use AAVSO report  if required.


The lastest version of ASTAP can display and report a light curve directly:


The light curve area has a pop-up menu to save it to file or copy it to the clipboard.

Here an example of an exoplanet transit measured using the blink&photometry tab:

A demonstration is available at YouTube:

Measure variable stars


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Inspector tab.

This tab is intended to measure accurately the tilt and curvature of your telescope & camera setup. It's done by calculating the best focus position for each image area. To do this it requires a series of images taken at several focuser positions.The routine will calculate from these images the best focus point of each area. It will measure the median HFD values of each image and area and build a table HFD as function of the focuser position. Form this data, curve fitting will give the transfer fucntion and the best focus position expressed in focuser steps. The focus point differences between the image areas will indicate the tilt of each area. The difference between the centrum and outer areas focus point will indicate the curvature.

The usage is as follows:


The reported hfd values can be selected and copied for further analysis in a spreadsheet.



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Mount analyse tab.

This tab is intended to study mount pointing accuracy.  The table will indicate the mount α, δ position and the image α, δ position in the selected equinox and the offset between them. 

Usage: take several images at different location in the sky. Load the images in the tab. Selected the desired equinox. Click on the button add the astrometric solutions. Study the result and if required select all rows, copy and paste the whole result to a spreadsheet for further analysis.

The images shall be of FITS format with the mount α, δ position in the header. This is normal the case. Keywords required RA, DEC or OBJCTRA, OBJCTDEC.

The solution can be written either in the orginal FITS file or in a seperate .wcss file.

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Live stacking tab.

All file(s) in the specified directory will be stacked live. If it is finished it will wait for new file(s). If a file is detected which is 0.2° away from the previous files a new stack will be started automatically. You can save the stack results from the viewer menu .

To identify files which are processed , they are renamed to the extension *.fts. You can rename them back with the button at the bottom.



Note there is no rejection of poor images. All images are added with equal influence:

Assuming the images are A,B,C,D, E... then

Simple serial stacking:

result1:=A
result2:=(result1+B )/2
result3:=(result2*2+C)/3
result4:=(result3*3+D)/4
result5:=(result4*4+E)/5


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Pixel math1 tab.

 Several options including background equalising.

Background equalization tool:


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Pixel math2 tab.

 Several options.

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Export FITS data to a spreadsheet:

To analyse the relation between the HFD value, focuser position, temperature and altitude it is possible to copy the data from a FITS image list to the operating system clipboard.

Just select a number of images, click on the  Analyse   button. Then select all relevant files and copy the data with right mouse button. Then copy the data into a spreadsheet for analysis.





Here and example of the result in a spreadheet:


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Viewer:



Viewer,  file menu

If the program is associated with FITS image files or any other format, it will show the image as soon you click image file. Only one instance of ASTAP will be allowed. After clicking on the second image it will be show in the first instance of ASTAP. If you want to open a second instance, just start ASTAP. If the program is started without parameters, you can open more instances.

Images can be loaded from the file menu or can be drag dropped on the main form.

Besides all FITS formats, the viewer support most image formats in 8/24 bit of 16/48 bit format. It can export to any FITS format and 16/48 bit PNG and TIFF formats.
ASTAP can display images and tables of MEF, multi-extension FITS. The images of MEF can be saved as a single image. The MEF tables can copied into the clipboard and paste to a spreadsheet. (v0.9.446)


This ASTAP version can import raw images from almost any digital camera, For this ASTAP executes a modified Libraw tool  "unprocessed_raw" which is included with the ASTAP for most editions. This special version export directly to FITS including date&time, Bayer pattern and active areas of the sensor only.  If "unprocessed_raw" is not included it can be installed in Linux by the "sudo apt-get install libraw-bin" command. 

File formats ASTAP8 bit16 bit32 bit
ImportFITS, JPEG, PNG, TIFFFITS, PNG, TIFF, PPM, PGM, raw formatsFITS, PFM
ExportFITS, JPEG, PNG, TIFFFITS, PNG, TIFF, PPM, PGMFITS, TIFF, PFM


The viewer has a preview function. After opening select "Preview FITS files". The preview is displayed in the ASTAP viewer. Use the arrow key to move up or down or just click on the image. The current zoom and position is maintained so you could study the corner of a series images on image quality.

The file open menu with preview selected:



Viewer,  file menu, thumbnail viewer for FITS files


ASTAP has a FITS thumbnail viewer (ctrl-T). This could be useful to browse your FITS files. By clicking on the thumbnail it will be opened in the viewer. With a right mouse button click some options are available as changing directory, copy, move, rename or rename to *.bak.

The thumbnail size is depending on the form size. Make it larger, the thumbnails will follow. Thumbnails are organized in 3*X. So the thumbnails are pretty big by purpose. The images are fully loaded in memory so it will consume some memory and time. So don't try get thumbnails of 400 images.




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ASTAP viewer screen shot:





Viewer menu Tools:


Viewer, tools, Astrometric solving the image in the viewer

  
With the   Solve|   button it is possible to find an astrometric solution of the image loaded. For this the estimated celestial center position α, δ should be available. This position is normally retrieved from the FITS header. Secondly the estimated image height in degrees should be specified in the stack menu, tab alignment.  In the same tab alignment you can specify the search radius and down sampling. For successful solving see conditions required for solving.

For solving JPG, PNG or RAW files it is possible to add the object position as center position using the deep sky database. Double click on the
δ position in viewer and enter the object name. The position will be retrieved from the database. This position will be used as a start point for the solver.



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Add SIP coefficients to the header

This option will add basic SIP polynome coefficients to the header to cope with 
basic barrel or pincushion distortion. In addition the image scale is adapted for the center undisturbed part only. The scale in the outer regions could be a fraction of a percentage different from the center of the image due to the distortion. Normally the scale factor is a compromise between the center and the slight disturbed outer regions.

The SIP correction can be tested with the option "Show distortion"


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Viewer, Tools, Batch processing:

With the batch routine several FITS image can be "astrometric solved" or converted. This conversion is not required for ASTAP. Automatic conversion is integrated in the menus.


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CCD inspector

The viewer has a CCD inspector under menu tools.  By reporting the median HFD value, sensor tilt and curvature the inspector will quickly show any problem of the imaging system. 

The image used for testing should be a single raw image with sufficient stars and not containing a disturbing large and bright deep sky object.  The exposure length should be long enough to image many stars but not too long preventing star saturation.

The routine will detect and annotate the stars with their HFD value and plot a tilt indicator in the image. A star rich image containing a few hunderd stars or more gives the best accuracy.

The following will be reported:





CCD inspector calculation method explained:




HFD 2D contour.

The star half flux diameters (HFD's) are displayed in a 2D contour. Dark areas indicate a lower and better HFD value. This will quickly visualise sensor tilt or other problems. To avoid false indications by outliers the HFD values are filtered by taking the median HFD value of the three closest stars and  allocate the result to all three stars. The HFD values are indicated numerical. They grey levels have no direct linea relation with the HFD.





HFD diagram.


The star HFD values can also be represented by areas of constant HFD. It is in principle a Voronoi diagram, but by  taking the median value of each three closest stars and allocate the median to the three stars it looks a little different.White areas indicate a star with an high HFD value. Darker areas indicate a lower value. The grey level is the HFD * 100.


HFD values

This tool will only indicate the median filtered HFD values next to the stars. The same values as in the 2D countour and HFD diagram. To avoid false indications by outliers the HFD values are filtered by taking the median HFD value of the three closest stars and  allocate the result to all three stars.


Median background values

This tools writes the median background values as numerical values in the image. Stars will be ignored but nebula will influence the background measurement..





Show distortion

This tools shows the difference between the Gaia star positions and the centroids of the imaged stars assuming a linear solution. A difference is indicated with a line 50 x larger then the actual difference in pixels. A scale is show at the left bottom. Also the  median astrometric error in arc seconds for the center 50% square (height/2 * height/2) is reported. This indicates the error to expect for astrometric measurements. Note the database resolution is
0.077"  in α and 0.039" in δ.

If SIP polynome as measuring mode is selected then the distortion will be partly corrected. The SIP polynome coefficients can be added by the tools option "Add SIP coefficients to the header". This correction will only work for basic barrel or pincushion distortion. You could also use the advanced SIP solution from Astrometry.net but select "order" three rather then the default two.

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Aberration Inspector

This tool creates a 3x3 mosaic of the images center, the corners and borders. This allows easy an comparison of the star shape at the different sections of the image.




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Viewer, Tools, Calibrate Photometry.

With this option the relation between flux and magnitude is measured. The image should be solved in advance to be able to calibrate the star flux with star database magnitudes. After the calibration is applied, the star magnitude at the mouse cursor is displayed. In the log an estimate for the limiting magnitude for point sources is reported for a detection limit of SNR ≥7.  The accuracy is better then ±,0.5 magnitudes. The aperture used for star flux measurement can be adapted in stack menu tab "photometry".

For stretched images the reported (limiting) magnitude will be less reliable. Use the popup menu option "online query" to request the magnitude of the point sources.



Viewer, Tools, SQM report based on an image



With this option the  SQM = sky background value relative to the stars is measured and expressed in magnitude per square arc second.  The image should be solved in advance to be able to calibrate the star flux with star database magnitudes. The reported value will be equal to a value reported by an Unihedron SQM-L meter.  Atmospheric extinction of the stars at lower altitudes will be compensated.

Some background information:

http://www.lightpollution.it/download/sqmreport.pdf

At zenith the measured star flux and sky background flux are defined as comparable and star light extinction is zeroed by subtracting 0.28 magnitudes from the calculated extinction. So at zenith the SQM brightness values are comparable to deepsky object brightness and can be expressed in magn/arcsec². At lower altitudes the star and deepsky flux are lower due to higher air mass and therefore higher extinction minus 0.28  is taking in account.

Pre-conditions
1) Image is astrometrical solved for flux-calibration against the star database.
2) The background value is larger then pedestal value. If not expose longer.
3) Entering a pedestal value increases the accuracy. (mean value of a dark)
4) Apply on single unprocessed raw images only or
    calibrate single images and apply zero for the pedestal value.
5) DSLR images could require additional preparations.
6) No large bright nebula should be visible.
7) Calculated altitude is correct. The altitude will be used for an atmospheric extinction correction of the star light.



Viewer, Tools, Magnitude (measured) annotation.

With this option the stars are annotated with the estimated magnitude.  The image should be solved in advance to be able to calibrate the star flux with star database magnitudes.

If the Johnson-V version of the star database (V17) is used, the results match very accurate with AAVSO charts as demonstrated below. Camera was an ASI1600 with only an UV-IR block filter:



For best accuracy the image should be monochrome and the Gaia Johnson-V star databases V17 should have been installed and selected. The image should have  taken with a Johnson-V filter or none (clear). Saturated stars will be ignored since it is not possible to measure then accurately.



In the left bottom corner of the image an estimate for the limiting magnitude for point sources is reported using a detection limit SNR ≥ 7. Below this value detection of point source detection becomes unreliable.
The accuracy is better then ±,0.5 magnitudes. The image should not be stretched. The aperture used for star flux measurement can be adapted in stack menu tab "photometry". Results can be validated by requesting the Gaia BP magnitude magnitude of the faintest stars in the image using the popup menu option "online query".

For stretched images the reported limiting magnitude will be less reliable. Use
the popup menu option "online query" to request the magnitude of the faintest sources.


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Viewer, Tools, Star (database) magnitude.

With this option the stars are annotated with the star database magnitude. This can be done best with V17 containing the calculated Johnson-V magnitudes.

For a G-database the indicated magnitude is Gaia blue. For a V-database the indicated magnitude is Johnson-V  and the following the difference between Gaia blue and red,  positive for reddish objects. All in 1/10 of a magnitude.

Below, the image is 1) solved, 2) auto calibrated (using the V16)   The cursor is at a star and based on the flux of all know stars, the star Johnson-V magnitude is estimated to be 16.1. The stars are marked with the Johnson-V magnitude and  Bp-Rp color indication.

See also blink and photometry




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Viewer, Tools, Unknown star magnitude

Any unknown object or a star with an abnormal magnitude is identified. This option is intended to mark nova and minor planets using the star database. Any star like object missing from the star database will be marked. Also if the measured magnitude is one magnitude brighter then the database. The H18 star database up to magnitude 18 is recommended for this option. If the H18 is selected then missing object up to magnitude 17 will be detected. The image should be solved in advance.


Viewer, Tools, Variable star annotation

Variable star are annotated using the variable_stars.csv database.



Viewer, Tools, Asteroid and comet annotation

This option will annotate asteroids using the orbital elements taken from the MPCORB.DAT file and for comets the ComeEls.txt from the Minor Planet Center.

Usage:

- Solve an image.
- Go to to the viewer "Tools" menu, "Asteroid annotation".
- First time download the full MPCORB.DAT from the minor planet center. Link is available from the blue down arrow. Set the path to MPCORB.DAT correct.
- Set the limiting magnitude and maximum number of asteroids to read.
- Press the button   Asteroid & comet annotation   .

Remarks:

Renew the MPCORB.DAT and CometEls.txt  files every few months.

The observation date and time are extracted from the FITS header (date-obs, date-avg) or for other files the file date is taken.  If date average is not available it will be calculated from the exposure time and date-obs from the FITS header.

The latitude and longitude of the observation location are also taken from the header. If not available enter them manually or leave them at 0.


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Viewer, Tools, Deep sky annotations  

If the image is solved, it is possible to add deep sky annotations. See pull-down menu TOOLS:



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View menu

This menu has the following options:
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FITS tables

The viewer has limited support for displaying FITS binary and ASCII tables. It can read and write binary tables and read ASCII tables only. They are displayed in the memo. Values are separated by a tab #9 and can be selected and copied to a spreadsheet. It can display only one table and will display the first table only. The file can be saved again but all binary values will be all written as 4 byte float.

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Viewer popup menu:



Add annotation,  free text label at a x,y position. It can be connected via a line by first holding the right mouse button and moving the mouse away. See sample above.  Persistent by annotation keyword in the FITS header. The annotation can be switched off in pulldown menu "View". Remove by removing the annotation line in the header.  If a @ is added to the text, the annotation is written persistent in the image data. So the image will be permanently altered after saving. Adding two or more @ will increase the font size.

Add marker,
rectangle marker at x,y position. Draw the rectangle first by holding the right mouse button down and moving the mouse away. See sample above. The Persistent by annotation keyword in the FITS header. The annotation can be switched off in pulldown menu "View". Remove by removing the annotation line in the header.

Add object position, Enabled after astrometric solve. Will add the α, δ at the mouse position. Orange if a lock is possible, see above sample, red if not. Not persistent after image clean up.

Add marker at  α,  δ position, will place a yellow square at the specified α,  δ position.  See above sample for orange star. Enabled after astrometric solve. Persistent. Position will be saved with "save settings". If a C is typed, the marker is placed at the center.

Measure total magnitude within rectangle, Enabled after astrometric solve. The program will measure the flux and try to estimate the magnitude. Hold the right mouse down and pull a rectangle around the deep sky object, release mouse button and then select this menu.  For best accuracy the image should be monochrome and one of the Johnson-V star databases should have be installed and selected (V16 or V17). The image could have been taken with a Johnson-V filter for best results or none. The measured pixel values should be below saturation.



A demonstration is available at YouTube:  Photometry in the viewer

The measuring principle is as follows:
  1. Use the star database to measure the MEDIAN relation between flux of the detected stars and star magnitude from the database. (That's why solving is required and best result are achieved with the V16 or V17 Johnson-V star databases based on Gaia DR2) 
  2. Measure the MEDIAN background 1 to 10 pixels wide outside the rectangle box. This median measurement will ignore stars in the field.
  3. Measure the MEAN  flux inside the box.
  4. Calculate the magnitude for the "inside mean flux" minus "median outside box flux" using the relation found for the stars.

 You could argue that a Johnson-V filter or green channel is required for the image but in practice the error is limited depending on the spectrum.



Remove all markers and labels
. Will remove all none persistent labels.  Persistent annotations can be switches off in the viewer pulldown menu VIEW.

Copy image (selection) to the clipboard, copies the displayed image or a selection of the image to the clipboard. The orientation is depending on the selection direction.. (v0.9.417)
Copy position to clipboard, Enabled after astrometric solve. Copies the α,  δ position to the clipboard.
Copy position to clipboard in ° , Enabled after astrometric solve. Copies the α,  δ position in degrees to the clipboard.


Online query.
Query the Simbad database or Gaia database for all objects within the selected rectangle.

Remove deep sky  object. Removes an deep sky object as part of the pixel math tab routine "equalise background tool".  Hold the right mouse down and pull a rectangle around the deep sky object, release mouse button and then and then select this menu.

Local adjustments
Local colour smooth

Local remove colour.

Local Gaussian blur.

Local equalise tool.

Brighten a small area based on the corner values.

Gradient removal tool

To remove a linear gradient caused by light pollution or twilight. The routine need two empty areas 40x40 pixels in the image to measure the gradient. The area may contain stars but no deepsky object. The area are selected by pressing the right mouse button(first area) and while holding the mouse button move to the second area in the direction of the gradient. Then select in the popup menu "Gradient removal tool". Try to maximise the distance ideally the full image range.




Copy paste tool

Powerful touch-up tool  for cosmetic corrections. Small sections of the image can be copied as pasted on hot pixels or artifacts. Select the good part by holding the right mouse button and pulling a rectangle with the mouse and move the copied part to the part to be touched up..


Set area

Set an area for the colour replacement tool in tab pixel math 1.


Remove borders. This menu allows to remove parts of the image near de borders.

Crop fits image. This allows the crop the image. Hold the right mouse down and pull a rectangle, release mouse button and then and the select this menu

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Other popup menus:

Search for an object position:



Copy histogram values to clipboard. You can paste them then in a spreadsheet.


Fits header editor


Status bar. You can select to display the HFD and FWHM in arc seconds.



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Usage as astrometric solver and command line options:

For images in the viewer:

The simplest way to solve an image is just to load an image in the viewer and hit the solve button. Some settings are available in the   ∑   menu under tab alignment. 


The solution will be added to the fits header and center of the image will be displayed in the log of the  ∑   menu. Click on the save button to save the FITS file with the solution. With the solution, the status bar will show the astronomical position of the mouse pointer.

Conditions required for solving:

Quick checklist for solving:
  1. An approximate celestial position is specified (for a spiral search). This position should be displayed in the left top of the viewer menu. (unless you do a 180 degrees search)
  2. Correct image height in degrees specified within preferable 5% accuracy. This height (width x height) should be displayed in the status bar of the viewer and in tab alignment under "Field of view (height)" (Check focal length, sensor size settings or try FOV=auto once)" You can set/force a "Field of view (height)" in tab Alignment.
  3. At least 30 stars are visible. For small field-of-view (<1°) and away from the Milky-Way-plane expose longer about 30 to 300 seconds and use the H18 star database.
  4. Reasonable round stars and camera in focus.
  5. Image dimensions at least 1280x960 pixels. For smaller dimensions solving is still possible if the image quality is good.
  6. Image is not stretched, very saturated or heavily photo-shopped.
If you still have problems with solving, you could send me a link to the file involved (FITS is preferred) and if I have time I could have a look. Upload it e.g. to http://nova.astrometry.net or https://ufile.io/ and give me the link. For privacy reasons, prior to uploading you could remove your latitude/longitude information from the header using the viewer "Tools", "Batch processing", "Remove longitude latitude information" menu.

The internal astrometric solver works best with raw unstretched and sharp images of sufficient resolution where stars can be very faint. Heavily stretched, saturated, out-of-focus or photo shopped images are problematic. It requires minimum about 30 stars in the image to solve. Images containing of a few hundred stars stars are ideal. For star rich images, the program will reduce the detection limit to limit the number of stars. This will only work for unstretched images where brighter stars have a greater intensity then fainter stars. So ASTAP requires three star dimensions for solving. The star x, y coordinates and star intensity. Oval stars due to tracking errors or severe optical distortion will be ignored and solving could fail.

Check list for successful solving with ASTAP:
  1. An approximate α and δ celestial position is specified (for a spiral search). For FITS file this is normally read from the FITS file header and set automatically. The position can also be passed by the command-line. In case you view an JPEG, TIFF image, double click on α input to search for a know deep sky object position from the database.
  2. Correct image height in degrees specified within preferable 5% accuracy.  See ∑ window, tab alignment, group-box astrometric settings, "Field of view (height)". For FITS images this is normally automatic calculated from info in the file header. In cause of doubt you could try "Field of view (height)"=AUTO
  3. At least 30 stars are visible in the image. They can be very faint, barely visible in the noise. For large field-of-view (>1°) expose 5 to 10 seconds but for small field-of-view (<1°) far away from the Milky-Way plane you have to exposure longer 30 to 300 seconds and use the H18 star database.
  4. Reasonable round stars and the camera in focus. You could verify the star detection by the CCD inspector or by  the  Test button to show quads  in the  ∑   window, tab alignment). Most stars should be detected.
  5. Image dimensions at least 1280x960 pixels. Set downsample at 0 (=auto) and the program will select a downsampling factor automatically. Image height in pixels after ASTAP dowsampling should be somewhere between 1000 and 3000.
  6. Image is not stretched, very saturated or heavily photo-shopped. The total exposure time could be hours as long it is possible to separate the brightest stars from the faint by intensity.
  7. Search radius should be set large enough. See  ∑   window, tab alignment, group-box astrometric settings.  You could set this at 30° or for blind solving at 180°.
  8. Use downsample factor 0 (auto) or 2 for raw DSLR/OSC images. See  ∑   window, tab alignment, group-box astrometric settings. Save settings if modified (Viewer pull down menu, file, exit (and save settings). 
  9. If your image is full of hot pixels you could adjust the "Ignore stars less then["]"  in tab Alignment. This is set default at 1.5" but could be set higher for a long focal length.
  10. An other option for hot pixels is option "calibrate prior to solving". Select in the darks tab, a dark or darks with similar exposure duration as the lights you trying to solve. If your select several darks with  different exposure length, check-mark the option classify, "Dark exposure time". 
  11. The maximum number of stars to use should be defined. Typical set at 500. See ∑ window, tab alignment.
  12. Hash code tolerance should be defined. Typical set at 0.007. See tab alignment.
  13. For some solver failures you could force in ASTAP the option "slow" (-speed)  for more reliable solving. The reliability will be very high but solving will be slower.
  14. In case of excellent seeing the imaged star could be smaller then 1.5".  Reduce the setting "Ignore stars less then 1.5" in tab "Alignment". Star size should 2 pixels or more. Adapt downsampling accordingly. Improvements will be reported by a increased number of quad matches.
  15. For a field of view less then 60 arc minutes (long focal length) it is recommend to install the H18 star database and remove the H17 (or force use of the H18 in tab alignment). 
  16. If a global cluster fills the whole field, ASTAP could struggle to solve. Forcing option "slow" could  help.
  17. Best input format is FITS, RAW or 16 bit PNG, TIFF. JPEG compression or 8 bit PNG, TIFF files are a disadvantage.


Warnings:
In the plane of the Milky-way plane it is easy to image enough stars for solving as shown in this ESA image showing the sky star density. If you look outside the Milky-Way plane into deep space there are less stars. The G17 will contain enough stars if your field-of-view is 0.5 degrees or more. For a smaller field-of-view you have to exposure longer to image fainter stars. The H18 could work well up to a field-of-view of 0.25 degrees is exposed enough. For large field-of-view (>1°) expose 5 to 10 seconds but for smal field-of-view (<0.3°) you have to exposure longer 30 to 300 seconds. Expose long enough till the solver detects 30-50 stars minimum or till the solver gives a warning "Star database limit reached" indicating you have reached magnitude 18.




The maximum number of stars is set at 500. For very long exposures and a FOV below one degree a reduction of the maximum number of stars used could be required. Otherwise stars too faint for the database could result in a solving failure.




Database usability:


The first letter indicates the type of database. G indicates 10x10 degrees tiles and a single magnitude Gaia blue. V indicates 10x10 degrees tiles but Johnson-V magnitude and additional the magnitude difference of Gaia Blue and Gaia red.  The H indicates 5x5 degrees tiles and a single magnitude Gaia blue. The numbers 17, 18 indicate the maximum magnitude.


Support is available via the ASTAP Forum

Command line, ASTAP style

The program can be executed using command line options to solve images astrometric . E.g.  ASTAP -f  home/test/2.fits   -r 30 

The program will accept FITS files, JPG, PNG, BMP, XISF or TIF files.



ASTAP astrometric solver command line
The FOV, RA,DEC options are intended for none FITS files.
Not required for FITS files having the values in the header.
command
parameter unit remarks
-h

help info
-help

help info
-f file_name
File to solve astrometric.
-fstdinWill accept raw images via stdin. Raw format according INDI. See 1)
-r radius_search_field degrees The program will search in a square spiral around the start position up to this radius *
-fov field_height_of_image degrees Optional. Normally calculated from FITS header. Use value 0 for auto.  If 0 is specified the fov found by solving it will be saved for next time.(learn mode)  *
-ra center_right_ascension hours Optional start value. Normally calculated from FITS header.
-spd center_south_pole_distance
(dec+90)
degrees Normally calculated from FITS header *
The declination is given in south pole distance, so always positive.
-z down_sample_factor
0,1,2,3,4 Down sample prior to solving. Also called binning. A value "0" will result in auto selection downsampling. *
-s max_number_of_stars
Limits the number of star used for the solution. Typical value 500. *
-t tolerance
Tolerance used to compare quads. Typical value  0.007. *
-mminimum star sizearcsecThis could be used to filter out hot pixels.
-speed mode
slow / auto "slow" is forcing of reading a larger area from the star database (more overlap)  to improve detection. *
-o file

Name the output files with this base path & file name
-dpathSpecify a path to the star database
-analysesnr_minimumAnalyse only and report HFD. Windows: errorlevel is the median HFD * 100M + number of stars used. So the HFD is trunc(errorlevel/1M)/100.
For Linux and macOS the info is send to stdout only.
-analyse2snr_minimumBoth analyse and solve the image
-extractsnr_minimumAs analyse option but additionally write a .csv file with the detected stars info.
-sqmpedestalmeasure the sky background value in magn/arcsec2    relative to the stars. The pedestal is the mean value of a dark.
-focus1 file1.fits -focus2 file2.fits .......Find best focus point for four or more images using curve fitting. Windows: errorlevel is focuspos*1E4 + rem.error*1E3. Linux: see stdout
-annotateProduce a deep sky annotated jpeg file with same name as input file extended with _annotated *
-debugShow GUI and stop prior to solving
-logWrite solver log to file with extension .log
-tofitsbinning1,2,3,4Produce binned FITS file from input png/jpg *
-update

Update the fits header with the found solution *
-wcs


Write a .wcs file  in similar format as Astrometry.net. Else text style.



* Defaults can be set in the program. Shortcut CTRL-A, tab alignment
        

Commandline parameters have priority above fits header values. Front-end programs should provide access to -z and -r options. Default value for -z should be 0 (auto).


Typical command lines:

astap.exe -f image.fits  -r 50 

astap.exe -f c:\images\image.png  -ra 23.000  -spd 179.000  -fov 1.3  -r 50 


For most FITS files the command line can be short since telescope position and field of view can be retrieved from the FITS header. If a FITS file is not available, preference is a non lossless image format like .PNG or .TIFF or RAW like .CR2.  If possible in 16 bit or original 12 bit format. Not stretched or saturated, as raw as possible. For formats other then FITS the RA,DEC position and -fov (image HEIGHT in degrees !!) should be added.

If the FOV (image height in degrees)  is unspecified in the command-line for RAW, PNG, TIFF files, ASTAP will use the FOV as set in the program, stack menu, tab alignment. This setting can be learned and updated automatically with the parameters -fov 0. ASTAP will try all FOV between 10 degrees and and 0.5 degrees. E.g.

    astap.exe -f c:\images\image.png  -ra 23.000  -spd 179.000   -r 30 -fov 0

After a successful solve, the correct FOV will be stored in the ASTAP settings. For the next solve using images from the same source the -fov 0 parameters can be omitted and solving will be fast.

The debug option allows to set some solving parameters in the GUI (graphical user interface) and to test the commandline. In debug mode all commandline parameters are set and the specified image is shown in the viewer. Only the solve command has to be given manually:

    astap.exe -f c:\images\image.png  -ra 23.000  -spd 179.000   -r 30 -debug

or

    astap.exe -debug

1) The astap -f stdin command line option

Raw format send via stdin should start with three longwords (of 4 bytes). The first longword contains a format identification. The second longword contains the image width. The third longword contains the image height followed by the image raw data.

Raw format identification:

$31574152 or RAW1,  8bit mono image
$32574152 or RAW2, 16it mono image
$33574152 or RAW3, 24bit RGB image (R,G,B,R,G,B,R.....)
$43574152 or RAW4, 32 bit mono image
$66574152 or RAWf, 32 bit float mono image

The result is written to stdout. Only for the standard ASTAP Windows version the stdout is blocked (unless you use the command line version) and the result is written to a stdin.ini file at the ASTAP program directory. Use the -o command to specify any other file and directory. The .wcs file is always written but also here use the -o option to specify path and file name.

The ra,dec and fov should be specified in the command line. Example using a raw file as input:

e.g. /opt/astap/astap -f stdin -ra 23 -spd 179 -fov 1.2 -r 30 <./m42.raw


raw sample file which will solve using
/opt/astap/astap -f stdin -ra 6 -spd 95 -fov 2.8 -r 30 <./16bit_rosette.raw


Loading of the image can be tested by adding -debug to the command line

Command-line, output files

In command line mode the program produces two output files at the same location as the input image. In case a solution is found it will write a .wcs file 1) containing the solved FITS header only.  In any case it will write an INI file using the standard FITS keywords.

Example of the INI output file after an successful solve:

PLTSOLVD=T                                     // T=true, F=false
CRPIX1= 1.1645000000000000E+003               
// X of reference & centre pixel
CRPIX2= 8.8050000000000000E+002                // Y of reference & centre pixel  
CRVAL1= 1.5463033992314939E+002                // RA (J2000) of the reference pixel [deg]                   

CRVAL2= 2.2039358425145043E+001                // DEC (J2000)of the reference pixel [deg]                   
CDELT1=-7.4798001762187193E-004                // X pixel size [deg]
CDELT2= 7.4845252983311850E-004                // Y pixel size [deg]
CROTA1=-1.1668387329628058E+000                // Image twist of X axis [deg]
CROTA2=-1.1900321176194073E+000                // Image twist of Y axis [deg]                
CD1_1=-7.4781868711882519E-004                 // CD matrix to convert (x,y) to (Ra, Dec)  
CD1_2= 1.5241315209850368E-005                
// CD matrix to convert (x,y) to (Ra, Dec)                                   
CD2_1= 1.5534412042060001E-005                 
// CD matrix to convert (x,y) to (Ra, Dec)             
CD2_2= 7.4829732842251226E-004                 // CD matrix to convert (x,y) to (Ra, Dec)
CMDLINE=......                                 // Text message containing command line used
WARNING=......                                 // Text message containing warning(s)


The reference pixel is always specified for the centre of the image. The decimal separator is always a dot as for FITS headers.

Example of the INI output file in case of solve failure:

PLTSOLVD=F                                     // T=true, F=false
CMDLINE=......                                 // Text message containing command line used
ERROR= .....                                   // Text message containing any error(s). Same as exit code errors
WARNING= .....
                                // Text message containing any warnings(s)

The .wcs file contains the original FITS header with the solution added. No data, just the header. Any warning is added to the .wcs file using the keyword WARNING. This warning could be presented to the user for information.

1) Note the wcs file is default written as text file using carriage return and line feed for each line and is not conform the FITS standard. To have .wcs file conform the FITS standard add the command-line option -wcs.


Command-line, error codes

In the command-line mode errors are reported by an error code / errorlevel {%errorlevel%}. This is the same error as reported in the .ini file in case of failure.

Error codeDescribtion
0No errors
1No solution
2Not enough stars detected
16Error reading image file
32No star database found
33Error reading star database

To analyse a FITS file you could do in a Windows batch file the following:

c:\astap.fpc\astap.exe -f  c:\astap.fpc\test_files\command_line_test\m16.fit -analyse 30
echo Exit Code is %errorlevel%
pause

You will get
Exit Code is 326000666

where the HFD is 3.26 using 666 stars

For Linux and Mac a stdout is used reporting as follows:
HFD_MEDIAN=3.3
STARS=666
-analyse functionality:
ProgramWindowsLinuxmacOS
astapexit codestdoutstdout
astap_cliexit code & stdoutstdoutstdout




Finding best focus based on four or more input images:

c:\astap.fpc\astap -focus1 D:\temp\FocusSample\FOCUS04689.fit -focus2 D:\temp\FocusSample\FOCUS05039.fit -focus3 D:\temp\FocusSample\FOCUS05389.fit -focus4 D:\temp\FocusSample\FOCUS05739.fit -focus5 D:\temp\FocusSample\FOCUS06089.fit -focus6 D:\temp\FocusSample\FOCUS06439.fit -focus7 D:\temp\FocusSample\FOCUS06789.fit -focus8 D:\temp\FocusSample\FOCUS07139.fit
echo Exit Code is %errorlevel%
pause

or with the -debug option

astap.exe  -debug -focus1 D:\temp\FocusSample\FOCUS04689.fit -focus2 D:\temp\FocusSample\FOCUS05039.fit -focus3 D:\temp\FocusSample\FOCUS05389.fit -focus4 D:\temp\FocusSample\FOCUS05739.fit -focus5 D:\temp\FocusSample\FOCUS06089.fit -focus6 D:\temp\FocusSample\FOCUS06439.fit -focus7 D:\temp\FocusSample\FOCUS06789.fit -focus8 D:\temp\FocusSample\FOCUS07139.fit

Or with the special command line version:



Command-line pop-up notifier

If the ASTAP is command-line executed in MS-Windows, it will be shown by a small ASTAP tray icon on the right side of the status bar. If you move the mouse to the ASTAP tray icon, the hint will show the search radius reached. To refresh the value move the mouse away and back. 

If the search spiral has reached a distance more then 2 degrees from the start position then a popup notifier will show the actual search distance and solver settings:

  1. The first line indicates the search spiral distance (8º) from the start position and the maximum search radius (90º)
  2. The image height in degrees. 
  3. Downsample setting and the input dimensions of the image to solve. 
  4. The α and δ of the start position. 
  5. Speed normal (▶▶)  or small steps (▶)


See conditions required for solving to fix solve failures.

Tray icons are default off in the latest Win10 version. To set the ASTAP tray icon on, start a solve via the imaging program, go to Windows  "Settings", "Taskbar", "Turn system icons on or off" and set the ASTAP tray icon permanent "on" as shown below:

Blind solving performance

Blind solving performance for a 90 degrees offset:

ASTAP blind solver performance. Solving a 50 seconds exposed monochrome image of M24, 2328x1760 pixels covering a field of 1.75 x 1.32° starting 90 degrees more north at position 18:17, +72d 00 



Maximum stars set Tolerance set Astrometric solving  time
500 0.005 147 sec.
250 0.005 103 sec
150 0.005 92 sec
100 0.005 70 sec



Reducing the "maximum number of stars to use" will result in a faster solving but also an increased risk of solve failure.


Usage as a solver with other programs or as PlateSolve2 substitute

Back to index


CCDCIEL, using ASTAP as solver.

ASTAP is a menu option in the CCDCIEL program. Install both ASTAP and the H18 or H17 star database. Select in CCDCiel  menu ASTAP as solver and follow the guidelines in the help file. 

Progress is shown in tray icon and popup notifier.

Solving should be reliable. In case of failure, have a look to conditions required for solving.

Back to index


APT: using ASTAP as solver

ASTAP is fully supported since the release of APT version 3.85.1 

1) Install ASTAP program to the default directory.
2)  Install the H18 to the default directory.

In APT:
3) In point craft select ASTAP as solver.
4) In "Tools", "Object calculator" set the focal length and "CCD width x height" correctly.

5) Test solving with a saved image.


Progress is shown in tray icon and popup notifier.  In case of solve failure please check the FOV indicated. 

Solving should be reliable. In case of failure, have a look to conditions required for solving.

For older APT, Astro Photography Tool use ASTAP as a PlateSolve2 substitute by renaming ASTAP.EXE program as Platesolve2.exe. and select it as PlateSolve2:


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ModelCreator:

Installation as solver for ModelCreator:

  1. Install ASTAP and additional install the H18 star database. 
  2. In ModelCreator select ASTAP as plate solver.

Solving should be reliable. In case of failure, have a look to conditions required for solving.

Back to index


NINA, Nighttime Imaging ‘N’ Astronomy

For NINA version 1.9
  1. Install ASTAP and additional the H18 star database.
  2. Other settings as below:

To modify the ASTAP default settings, see astrometric_solving

Solving progress is shown in tray icon and popup notifier.

Solving should be reliable. In case of failure, have a look to conditions required for solving.

Back to index


Back to index


SharpCap:

Installation as solver for SharpCap:

  1. Install ASTAP and additional install the H18 star database.
  2. In SharpCap select ASTAP as plate solver.

Solving should be reliable. In case of failure, have a look to conditions required for solving.


Back to index


SGP, Sequence Generator Pro:

The latest SGP versions support ASTAP as solver. Just install ASTAP and H18 database. Select ASTAP as solver. Set binning at 1x1 or 2x2. See conditions required for solving.

Solving progress is shown in tray icon and popup notifier.

Solving should be reliable. In case of failure, have a look to conditions required for solving.

For older SGP versions: you could use ASTAP as PlateSolve2 substitute:

The orginal PlateSolve2.exe is located at C:\Users\you\AppData\Local\SequenceGenerator\     Where "you" is your user name.  You can access this directory also directly by %LOCALAPPDATA%\SequenceGenerator

  1. Install ASTAP and additional install the G17 star database in the same directory. Typical c:\program files\astap
  2. Copy or move the astap.exe  and all 290 files with extension .290  to C:\Users\you\AppData\Local\SequenceGenerator\
  3. Rename the original Platesolve2.exe to something like PlateSolve2ORG.exe
  4. Rename ASTAP.exe to PlateSolve2.exe
  5. Test it with SGP. The confidence will be always 999. No PlateSolve2 window will be shown.

Progress is shown in tray icon and popup notifier.

If you select in SGP the PlateSolve2 setting "Max Regions" (=3000) this will force a search up to 90 degrees diameter. However the solver will be most likely stopped halfway by a SGP timeout.

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Voyager:

The latest Voyager versions support ASTAP as solver. Just install ASTAP and H18 database. Select ASTAP as solver.

Solving progress is shown in tray icon and popup notifier.

Solving should be reliable. In case of failure, have a look to conditions required for solving.

For older Voyager versions: you could use ASTAP as PlateSolve2 substitute. The original PlateSolve2.exe is located at  C:\Program Files (x86)\Voyager 

  1. Install ASTAP and additional install the G17 star database in the same directory. Typical c:\program files\astap
  2. Copy or move the astap.exe  and all 290 files with extension .290  to  C:\Program Files (x86)\Voyager
  3. Rename the original  Platesolve2.exe to something like PlateSolve2ORG.exe
  4. Rename ASTAP.exe to PlateSolve2.exe
  5. Test it with Voyager. E.g. in the OnTheFly section. Confidence will be reported as 999.  E.g. Solved (J2000) => RA 19 59 36,167  DEC 22 42 36,31  PA 277,4 Res. 1,17 [as/px] FL 1131,77 [mm] Star/s 999

Back to index




Installation of the external Astrometry.net solver:

MS-Windows:

Install a local copy of Astrometry.net (via ANSVR  or  Astrotortilla)   as the astrometric solver. Or alternatively if you have Win10, 64 bit Creation edition you use the new Linux sub-system


ANSVR: The ANSVR link contains a newer compilation of astrometry.net made for SGP. It runs as a Linux program under Cygwin in MSWindows. Follow up to installation step 9. The link you have to put in ASTAP is as follows:

C:\Users\user_name\AppData\Local\cygwin_ansvr\bin\bash.exe     

Adapt "user_name" to the login name used in Windows.

The server program ANSVR is not required. Remove the ANSVR shortcut in the startup menu. Location:

C:\Users\user_name\AppData\Roaming\Microsoft\Windows\Start Menu\Programs\Startup


Alternative Linux sub-system in Win10 64bit Creators edition

Path for the astrometry.net solver program
ANSVR installation:
    C:\Users\user_name\AppData\Local\cygwin_ansvr\bin\bash.exe
Astrotortilla installation:
    C:\cygwin\bin\bash.exe
Win10 subsystem:
    C:\Windows\System32\bash.exe


Linux installation:
The single executable astap could be used anywhere. Standard directory could be c:/opt/astap but also at your home folder.

If you want to use  astrometry.net  this is described at installation. To get the Astrometry.net solver type: sudo apt-get install libcairo2-dev libnetpbm10-dev netpbm libpng-dev libjpeg-dev python-numpy python-pyfits python-dev zlib1g-dev libbz2-dev swig libcfitsio-dev   You also have to download index files.

Path to the astrometry.net solver program "solve-field" could be:

/usr/bin/
or
/usr/local/astrometry/bin



Appendix 1, the stack process:
The stacking process for one shot color color camera's will be mathematically executed as follows:

The master flat is calculated as:

master flat: = (1/n ∑ [flat] - 1/n ∑ [flat darks] )

Where a bias image could be used as flat-dark image. The master flat should be averaged by a 2x2mean to remove Bayer matrix artifacts.

Each image is calculated as:

(image- {∑ [darks]/n} ) / master flat

Then the Bayer matrix is applied and finally the images are stacked in mode average or sigma clipped.

So for average stack:

final image:= 1/n ∑ Bayer(image)

Back to index


Appendix 2, the 1476 star database format:

The .1476 format divides the sky in 1476 area's and 1476 corresponding files with the extension .1476. The 1476 areas have a minimum width or diameter of 90°/17.5 equals 5.143°.  The boundaries are defined by constant α and δ values. For the similar 290 file format see the HNSKY help file

Each star is stored in a record of 5 bytes. The files start 'with a 110 byte header containing a textual description and the record size binary stored in byte 110.  
The RA values are stored as a 3 bytes word. The DEC positions are stored as a two's complement (=standard), three bytes integer. The resolution of this three byte storage will be for RA: 360*60*60/((256*256*256)-1) = 0.077 arc seconds. For the DEC value it will be: 90*60*60/((128*256*256)-1) = 0.039 arc seconds.  The stars are sorted on magnitude and the magnitude is stored in a byte of the special preceding header with an offset to make all values positive.

  Example of star Sirius RA and DEC position:
  The RA position is stored as C3 06 48 equals: (195 +6*256 +72*256*256)*24/((256*256*256)-1)=6.75247662 hours equals: 6:45:8.9
  The DEC position is stored as D7 39 E8, equals: 215 57 -24. The DEC is then (215 +57*256 -24*256*256)*90/((128*256*256)-1)=-16.7161401 degrees equals -16d 42 58

Record format:

The 290-5 or 1476-5, short record size of 5 bytes for one star without designation:

    type
      hnskyhdr290 = packed record
        ra7  : byte;
        ra8  : byte;
        ra9  : byte;
        dec7 : byte;
        dec8 : byte;{magnitude and dec9 are written once in preceding header-record}
      end;



Stars are sorted from bright to faint in the "0.1" steps. Within the magnitude range, the stars are additional sorted in DEC. For a series of stars with the same DEC9 value, a header-record is preceding containing the DEC9 value stored at location DEC7. Since the stars are already sorted in 36 declination bands, the number of DEC9 values is already limited by a factor 36.

1476-5 header-record example: FF FF FF 20 06 This indicates the following records have a DEC9 value of 20 -128 offset and a magnitude of (06 - 16)/10 equals -1.0 (new method, +16 offset).

The shorter records methods become only space efficient for very large star collection of a few million stars. In these large collections many stars can be found with the same magnitude and DEC9 shortint. The Gaia database is only issued in the 1476-5 format of 5 bytes per star. or in an older format 290-6 (V17) or 290-5. The 290-6 has one more byte for the colour information. This is documented in the HNSKY planetarium program help file.

So the record sequence will be as follows:

header-record {new section will start with a different magnitude and dec9}
record
record
record
record
header-record  {new section will start with a different magnitude and dec9}
record
record


The 1476 areas: Each ring is divided by lines of constant RA such that the minimum width in RA is about 5 degrees (deltaRA*cos(DEC)

.
Declination minimum   Declination maximum Ring RA cells  RA step north[degr] RA step distance south[degr] DEC stepFiles
 -90.00000000  -87.42857143   0-1 1                       0101.1476                                    
-87.42857143 -82.28571429  1-2 3 5.38377964 16.10799190  -2.57142857  {=90/(2*17.5)}0201.1476, 0202.1476, 0203.1476
-82.28571429 -77.14285714  2-3 9 5.36933063 8.90083736    -5.14285714  {=90/17.5}0301.1476,  . . . . . , 0309.1476
-77.14285714 -72.00000000  3-4 15 5.34050241 7.41640786  -5.14285714  {=90/17.5}0401.1476,  . . . . . , 0415.1476
-72.00000000 -66.85714286  4-5 21 5.29743419 6.73757197  -5.142857140501.1476,  . . . . . , 0521.1476
-66.85714286 -61.71428571  5-6 27 5.24033376 6.31824883  -5.1428571406 . . .
-61.71428571 -56.57142857  6-7 33 5.16947632 6.00978525  -5.1428571407 . . .
-56.57142857 -51.42857143  7-8 38 5.21902403 5.90674549  -5.1428571408 . . .
-51.42857143 -46.28571429  8-9 43 5.21991462 5.78564078  -5.1428571409 . . .
-46.28571429 -41.14285714  9-10 48 5.18296987 5.64803600  -5.1428571410 . . .
-41.14285714 -36.00000000  10-11 52 5.21357169 5.60088688  -5.1428571411 . . .
-36.00000000 -30.85714286  11-12 56 5.20082354 5.51859939  -5.1428571412 . . .
-30.85714286 -25.71428571  12-13 60 5.15069276 5.40581321  -5.1428571413 . . .
-25.71428571 -20.57142857  13-14 63 5.14839353 5.34991355  -5.1428571414 . . .
-20.57142857 -15.42857143  14-15 65 5.18530082 5.33887123  -5.1428571415 . . .
-15.42857143 -10.28571429  15-16 67 5.17950194 5.28678585  -5.1428571416 . . .
-10.28571429 -5.14285714  16-17 68 5.20903900 5.27280509  -5.1428571417 . . .
-5.14285714 0.00000000  17-18 69 5.19638762 5.21739130  -5.1428571418 . . .
0.00000000 5.14285714  18-19 69 5.21739130 5.19638762  -5.1428571419 . . .
5.14285714 10.28571429  19-20 68 5.27280509 5.20903900  -5.1428571420 . . .
10.28571429 15.42857143    20-21 67 5.28678585 5.17950194  -5.1428571421 . . .
15.42857143 20.57142857  21-22 65 5.33887123 5.18530082  -5.1428571422 . . .
20.57142857 25.71428571  22-23 63 5.34991355 5.14839353  -5.1428571423 . . .
25.71428571 30.85714286  23-24 60 5.40581321 5.15069276  -5.1428571424 . . .
30.85714286 36.00000000  24-25 56 5.51859939 5.20082354  -5.1428571425 . . .
36.00000000 41.14285714  25-26 52 5.60088688 5.21357169  -5.1428571426 . . .
41.14285714 46.28571429  26-27 48 5.64803600 5.18296987  -5.1428571427 . . .
46.28571429 51.42857143  27-28 43 5.78564078 5.21991462  -5.1428571428 . . .
51.42857143 56.57142857  28-29 38 5.90674549 5.21902403  -5.1428571429 . . .
56.57142857 61.71428571  29-30 33 6.00978525 5.16947632  -5.1428571430 . . .
61.71428571 66.85714286  30-31 27 6.31824883 5.24033376  -5.1428571431 . . .
66.85714286 72.00000000  31-32 21 6.73757197 5.29743419  -5.1428571432 . . .
72.00000000 77.14285714  32-33 15 7.41640786 5.34050241  -5.1428571433 . . .
77.14285714 82.28571429  33-34 9 8.90083736 5.36933063  -5.1428571434 . . .
82.28571429 87.42857143  34-35 3 16.10799190 5.38377964  -5.142857143501.1476, 3502.1476, 3503.1476
87.42857143 90.00000000  36-37 1 3601.1476

The 1476 areas:


South pole view of the 1476 areas:


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Succes,  Han  K


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