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# what does "percent" curvature mean/how is it calculated?

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### #51 freestar8n

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Posted 17 January 2020 - 05:07 PM

Hi Frank,

But do you think the term "off-axis aberration" expressed in delta HFD from the center is appropriate?

Han

It is inherently problematic if it canâ€™t tell a well focused and guided image from one that isnâ€™t.

You need to factor in how small the stars are. Not just how different they are.

If the field is symmetric I would want to know central fwhm and outer fwhm. Just the difference or percent bloat doesnâ€™t tell me much.

Frank

### #52 han.k

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Posted 17 January 2020 - 05:21 PM

I don't want to express it in %. So if the center fwhm is 2.5 and the outer 3.5, I will report it as "off-axis aberration=1.0 fwhm"

Note for Gaussian star the hfd and fwhm are identical but hfd works better for non-Gaussian shaped stars.

Han

### #53 freestar8n

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Posted 17 January 2020 - 05:44 PM

I don't want to express it in %. So if the center fwhm is 2.5 and the outer 3.5, I will report it as "off-axis aberration=1.0 fwhm"

Note for Gaussian star the hfd and fwhm are identical but hfd works better for non-Gaussian shaped stars.

Han

I would not want to have 1.5 in center and 2.5 outer be considered the same as 9 center and 10 outer.

Both have a diff of 1. The first is good. The second is junk. Neither has anything to do with curvature.

Frank

### #54 han.k

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Posted 18 January 2020 - 05:19 AM

I would not want to have 1.5 in center and 2.5 outer be considered the same as 9 center and 10 outer.

Both have a diff of 1. The first is good. The second is junk. Neither has anything to do with curvature.

Frank

What would you suggest then?

You can't measure something like the curvature accurately with a single image since you don't know if it is in focus and have an unknown influence of the seeing.

You can only measure B (inner FWHM) and A (outer FWHM). For reporting there are three variants possible:

•     Report B and A
•     Report B and ((A/B)-1)*100% (The CCDinspecture curvature)
•     Report B and A - B = D

Only with a multiple image analyses you can report C and E accurately. Only C is an indication of the curvature.

Han

### #55 freestar8n

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Posted 18 January 2020 - 06:09 PM

What would you suggest then?

You can't measure something like the curvature accurately with a single image since you don't know if it is in focus and have an unknown influence of the seeing.

You can only measure B (inner FWHM) and A (outer FWHM). For reporting there are three variants possible:

•     Report B and A
•     Report B and ((A/B)-1)*100% (The CCDinspecture curvature)
•     Report B and A - B = D

Only with a multiple image analyses you can report C and E accurately. Only C is an indication of the curvature.

Han

If the goal is to measure the curvature of the image surface then I would find focus as a function of radius from the center and calculate the radius of the sphere that matches the best-focus surface.

But that would only tell me how the surface is curved.  It wouldn't tell me about coma and other aberrations that have a field dependence.  And it wouldn't tell me how sharp it is in the center.

Is the goal to make adjustments to the optics so the image is as flat as possible, or is it to make the entire image as sharp as possible?  Those are two different things.

Or maybe the goal is to measure the curvature of EdgeHD compared to ACF.  Would you want to measure curvature - or overall field sharpness?  Those are two different things.

I think what people really want is to be as sharp in the center as possible - and at the same time be sharp at the edges.  Getting sharp in the center amounts to collimation on a single star - and spacing adjustments on the optics, such as backfocus, won't affect that very much.  But spacings can have a big effect on field aberrations - mainly coma and astigmatism.

So I would make adjustments to spacings - if you need to - and collimate using a single star in the center - and measure its fwhm.  With a single star in the center it should be nearly diffraction limited - and the fwhm should be well under 1" using video.

Then make additional adjustments - hopefully small - so the field stars are uniformly aberrated around the edge - and measure their sizes.  You can express the final result as fwhm in the center and at the edge of the field of radius 15mm or whatever.

So that is 3 numbers:  fwhm in the center, fwhm at some distance from center - and what that distance is.

Since the edge bloat is due to a combination of aberrations - and not simply field curvature - it doesn't make sense to fit it to a sphere or parabola.  So I would just leave it like that.

Fortunately these "curvature" plots - which are often posted - show the center and edge fwhm's in the upper left - and that is the first thing I look at.  I see values like 5" and 8" or something - and that is so big it won't capture the range of aberration well at all.

And for showing the overall quality of the field - I want to see actual stars around the field.  Nowadays people commonly show the 3x3 tiled images that show zoomed in views around the image - and I think that works well - along with fwhm's in arc-seconds.

Frank

### #56 han.k

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Posted 19 January 2020 - 02:30 AM

Without a single image quality number, it will be very difficult to judge which of all these time consuming adjustments is the best compromise.

### #57 freestar8n

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Posted 19 January 2020 - 02:49 AM

Without a single image quality number, it will be very difficult to judge which of all these time consuming adjustments is the best compromise.

Many things are complex enough they can't be reduced to a single number.

If you want best results with your equipment you will need to balance and optimize many variables and their trade offs.

People like a single number and a single way to optimize it.  But the real world usually doesn't work that way.

One thing's for sure.  When I see an aberrated, defocused, and poorly guided image expressed as a single "curvature" value - I know that value doesn't tell me anyting.

Frank

### #58 bobzeq25

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Posted 19 January 2020 - 03:17 AM

Many things are complex enough they can't be reduced to a single number.

If you want best results with your equipment you will need to balance and optimize many variables and their trade offs.

People like a single number and a single way to optimize it.  But the real world usually doesn't work that way.

One thing's for sure.  When I see an aberrated, defocused, and poorly guided image expressed as a single "curvature" value - I know that value doesn't tell me anyting.

Frank

I'm trying to sort how much of my residual problem is tilt, and how much collimation.  My plan is to wait for the Baader tilt adjuster and play with that.  My images are pretty good now.

Edited by bobzeq25, 19 January 2020 - 03:18 AM.

### #59 han.k

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Posted 19 January 2020 - 03:55 AM

I'm trying to sort how much of my residual problem is tilt, and how much collimation.  My plan is to wait for the Baader tilt adjuster and play with that.  My images are pretty good now.

Reads like a good plan. Eliminate tilt. Achieve best colimation. Find best corrector distance if any.

Many things are complex enough they can't be reduced to a single number.

If you want best results with your equipment you will need to balance and optimize many variables and their trade offs.

People like a single number and a single way to optimize it.  But the real world usually doesn't work that way.

As an engineer, I beg to differ. Any decision process to select the best option/setting comes to a binary conclusion this is the best compromise. It's no magic. It's just a math model with weight factors for each quality to measure. The debate like this discussion is usually about the definition of the qualities to measure and weight factors to apply. Once they are defined the decision process is easy.

Han

Edited by han.k, 19 January 2020 - 06:20 AM.

### #60 ezwheels

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Posted 19 January 2020 - 12:12 PM

Agree Han,

If the optics engineers design a scope and reducer/flattener combination to have an optimized spacing of 65mm, you should start there because that math and those physics ™ are known, quantifiable and provable. Now, due to complexities in manufacturing and fabrication and material variances these numbers are usually good to within a few millimeters and using the method you are describing above helps the end user get that last bit of optimization that the scope is capable of. Those last mm's have a huge effect on some scope and reducer combinations and are easily mapped with stacking unguided 5-10 second star field images at or near zenith. By doing this you pretty much eliminate guiding errors, polar alignment errors and sagging errors and are left with optical train issues that can be mapped.

Frank, I am not, and I do not think anyone else here is, advocating for simply flattening the "curvature" map in CCDi at the expense of the central stars FWHM. CCDi lists curvature numbers and FWHM numbers for each measured frame or an average of multiple measured frames. When I adjust spacing for this I consider only the results where the "curvature" is minimal and the FWHM is the lowest or near the lowest. As flawed as the application may now be (it hasn't measurably been updated in the last decade at least as far as I can tell) it is all we have that was designed for this specific process. You can do similar things in PI, but they are plug-ins. I use both, but I am certain there is room for a new app, that is more sophisticated to fill this space.

edited to say: unguided 5-10 sec exposures

Edited by ezwheels, 19 January 2020 - 01:38 PM.

### #61 freestar8n

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Posted 19 January 2020 - 04:06 PM

Frank, I am not, and I do not think anyone else here is, advocating for simply flattening the "curvature" map in CCDi at the expense of the central stars FWHM. CCDi lists curvature numbers and FWHM numbers for each measured frame or an average of multiple measured frames. When I adjust spacing for this I consider only the results where the "curvature" is minimal and the FWHM is the lowest or near the lowest. As flawed as the application may now be (it hasn't measurably been updated in the last decade at least as far as I can tell) it is all we have that was designed for this specific process. You can do similar things in PI, but they are plug-ins. I use both, but I am certain there is room for a new app, that is more sophisticated to fill this space.

edited to say: unguided 5-10 sec exposures

When I see people post these curvature images I almost never see mention of the fwhm.  They just say "here's my curvature" and are either happy that it looks flat, or unhappy that it is distorted.

With cmos imaging cameras you can operate in video mode and interactively explore stars around the field at the diffraction limit, where aberrations show better.  There is no need to expose, download examine, tweak - and repeat.

The curvature map doesn't show the stars that were used for the map.  As mentioned above, I think the 3x3 tiled view showing the stars - along with measurements of the fwhms in a few place - is much better information.

Frank

### #62 ezwheels

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Posted 19 January 2020 - 05:59 PM

Frank, I absolutely agree on your observation about the posted curvature maps and I would hope that others are taking into account the method for getting those maps and the liabilities of focusing (pun intended) solely on the %curvature. And I agree on the 3x3 matrix, but I would have the theoretical application focus in each of the nine segments and give delta values in mm's for each corner from the best focus position of the central section. Then you could decide whether you have tilt or spacing induced "curvature" and where to make changes and how much at each corner. Until we have such an application, I would say that I can't make much use of video unless I had a second focuser and perhaps a motorized CTU in the train that can adjust spacing and tilt in real time. Otherwise, for "parabolic FWHM" you have to disconnect everything in the train and add or remove spacers, refocus and rinse and repeat. Video may help with adjusting tilt in real time if you are sitting at the scope with a laptop and an allan wrench tweaking the CTU.

### #63 han.k

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Posted 20 January 2020 - 03:10 PM

I have added today an inspector tab to ASTAP 0.9.313. With this tab you can analyse a series of images on hfd values of several areas. The program will read the focuser position from the header and measure the median hfd, center hfd (inner 25% image), outer hfd (25%) and the image split in four sections.

Usage:

• 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 a small step but only one way to prevent backlash problems. Images with stars having an hfd above 14 will not be analysed correctly since this was historically not implemented.
• Browse to the images.
• Press analyse
• Select all rows by ctrl+a, copy with ctrl+c and copy to your favorite spreadsheet.

Experimental.

My 100mm APO astrograph doesn't show any real problem. The hfd_center is a little shifted to the left.

The series of the 12"inch newton was from a UK amateur used for focus algorithm testing. You can see that the hfd_center is always shifted a little to the right indicating an curvature of a few focus steps.

Now I need other image series for testing.

Han

Edited by han.k, 20 January 2020 - 03:15 PM.

### #64 han.k

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Posted 21 January 2020 - 01:14 PM

In ASTAP version 0.9.314, I have added a hyperbole curve fitting routine to the inspector tab which find the best focus position for each area of the image using multiple images. The difference is expressed in focuser positions and should be a good representation of the curvature & tilt.

My focuser makes about 1500 steps per mm, so the found differences up to 150 steps are very small about 0.1 mm or 0.004 inch. So it would be good to have an other test set of a poorer performing telescope then my APO astrograph.

18:47:33  Finding the best focus position for each area using hyperbola curve fitting
18:47:47  median  Focus=36000 , a=1,58025 , b=189,90935
18:47:47  center  Focus=35950 , a=1,72525 , b=199,74451
18:47:48  outer_ring  Focus=36000 , a=1,33893 , b=167,36795
18:47:48  bottom_left  Focus=36000 , a=1,63600 , b=194,74364 offset: 50
18:47:48  bottom_right Focus=35863 , a=1,31063 , b=152,53939 offset: -88
18:47:48  top_left  Focus=36100 , a=1,08150 , b=126,90394 offset: 150
18:47:48  top_right  Focus=36000 , a=1,59440 , b=186,42191 offset: 50

Han

Below the measured curve and the curve fitting for the CENTER area of the image.

Below the measured curve and the curve fitting for the OUTER area of the image. Note that the dip of the real curve is less deep, indicating off-axis aberration.

### #65 ghulands

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Posted 21 January 2020 - 06:17 PM

In ASTAP version 0.9.314

Any chance you can post a new build for macOS?

### #66 han.k

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Posted 22 January 2020 - 05:24 PM

Any chance you can post a new build for macOS?

ASTAP version 0.9.315 is now available for macOS. Same for Linux and Windows. Please report any problems or findings. It is under development.

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.

My next test would be the testing of the repeatability, but the clouds just came in here so that has to wait.

Han

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