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Measuring tilt and curvature with best focus for each area

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With this post, I want to introduce a new method for measuring tilt and curvature and it is a request  for some test data.

Thanks, Han

The program  CCDinspecter measures the tilt and curvature by the difference in FHWM (~hfd) values between the center and outer areas of an image.  I have tried to indicate it in a sketch below:


I assume CCDinspecter calculates the curvature by ((A/B)-1)*100%. Where B is the average fwhm/hfd of the center and A of the outer areas. This will not work if the image is not in focus. There is even a focuser position where A=B. It would be better if the curvature would be measured as C expressed in focuser steps.

So ideally you should measure the best focus position for each area.  This can be realised by taking several images like for focusing and find the best focus point of each image area by curve fitting the V-curve of the hfd values measured in each area of the images.

This idea is implemented in the free program ASTAP, tab "inspector".  You can feed it with several images at different focus points and it will report the best focus point for each area of the image.  It is also  possible to copy paste the data into a spreadsheet. Then you create graphs like these:

Graph of the focus curves of  100mm APO astrograph, focal length 580 mm. Plotted are hfd values of median=all, the center of the image, outer area and the image split in four parts:





In the program, the data is presented as a table which can be selected and copied to the clipboard:



The usage is as follows:

  • Prepare a series of short exposure images with different focuser positions and a lot of stars. Exposure time a few seconds. Move for each image the focuser a small step but only in one way to prevent backlash problems. Images with stars having an hfd above 12-14 will not be analysed correctly since this was historically not implemented.
  • Browse with ASTAP to the images.
  • Press analyse
  • Optional:  Select all rows by ctrl+a, copy with ctrl+c and copy to your favorite spreadsheet.
  • Press curve fitting for report on best focus point for each image area.

This is experimental. I'm interested in more test images.  If anybody can assist, make them as indicated below.





For the images to analyse in the "inspector tab", please use a fixed focuser step since for all  curve offsets the same weight factor is used in curve fitting routine. It is possible to make more then one exposure per focuser position but do the same for all focuser positions.

For example if your focuser is focused around position 1007 and the range to reach hfd=12 on both sides is 900-1100 do the following:

move to 800 {to remove backlash}

move to 900 and make image of 5 or 10 seconds exposure

move to 910 and make image

move to 920 and make image




move to 1100 and make image

This makes 20 steps but probably 10 steps or even less will do. The direction is not important. You could also do 1100 to 900. You should also be able to mix the test series. The detection doesn't work above hfd=12 since it was designed for the alignment & solver and not finding the focus point.





Edited by han59
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It is possible to plot in an spreadsheet both the measured V-curve and the hyperbola fit as found:


Here an early report of my setup
13:22:39  median        Focus=35972    a=1,23909     b=143,37264    _____________        lowest error=0,01187     iteration_cycles=4
13:22:39  center        Focus=35925    a=1,87688     b=212,46136    _____________        lowest error=0,00540     iteration_cycles=4
13:22:39  outer ring        Focus=36028    a=0,30912     b= 37,90557    offset=  103        lowest error=0,02590     iteration_cycles=6
13:22:39  bottom left        Focus=36000    a=1,47225     b=169,40969    offset=   75        lowest error=0,01023     iteration_cycles=2
13:22:39  bottom right    Focus=35825    a=1,52325     b=167,86880    offset= -100        lowest error=0,00695     iteration_cycles=2
13:22:40  top left        Focus=36094    a=1,39523     b=159,90826    offset=  169        lowest error=0,00958     iteration_cycles=4
13:22:40  top right        Focus=35934    a=1,74906     b=200,38594    offset=    9        lowest error=0,00777     iteration_cycles=4

My focuser makes about 1500 steps per mm, so the found differences up to 169 steps are very small a little more then 0.1 mm or 0.004 inch.


The measured curve and the hyperbola fit of the INNER area



The measured curve and the hyperbola fit of the OUTER area:



The spreadsheet used is attached



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Thanks Han, that looks like it will be very useful. 😀


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