Fast Newtonian and Field Curvature Effect on Photometry?

If the coma corrector produces good images across the field of view that you use for your photometry, and you make and use good flats, your 10" f/3 Newtonian ought to be fine for photometry. If the field curvature produces noticibly poor images at the edges of the field, you would either use an intermediate focus position to make similarly soft images across the field or use the portion of the field that has sensibly good images. The total light in the images will be the same even if they are not the same image quality.

Hi, Mike:

Let's do a little math. Focal plane curvature in a Newtonian has a radius roughly equal to the mirror's focal length, so in this case the focal plane has a radius of curvature of 762mm. The IMX455 sensor has a diagonal size of 43mm. With some triangle math, that says that if you focus the center of the image, the corners will be 0.303mm away from focus.

Using the depth of focus calculator at astrofriend.eu, the depth of focus for a 10" f/3 telescope is 0.003mm (theoretical focus depth) or 0.03mm (based on typical seeing of 3 arcseconds). I'd suggest something around 0.01mm in order that focus blur isn't noticeably degrading your image.

Aperture photometry assumes that all stars have the same fraction of their point spread function contained within the aperture circle. If some stars have significantly different point spread functions due to defocus, that aperture photometry assumption has potentially been violated.

This suggests that at the corners you're more than an order of magnitude too curved to get away with not correcting curvature.

However, the IMX455 is giving you a huge field of view (almost 3-degrees x 1.5 degrees) with that scope. You probably don't need anything close to that FOV for photometry. (I've had a 14 arcmin x 14 arcmin field of view for the past 15 years with a 10" SCT and have had extremely few AAVSO program stars where I couldn't do effective photometry due to FOV limitations.) And so you might aggressively crop the IMX455 to a much smaller region of interest, significantly shrinking your field curvature issues. Or maybe wait until the new crop of cameras based on the Sony IMX571 monochrome comes out in the next few months, with the performance of IMX455 but in a sensor sized at APS-C (and with half the price tag).

- Mark

Hi there, I am in a similar situation as you, having recently completed my homemade 12.5" F/2.8 prime focus imaging scope. I use the QHY5iii CMOS and my Canon 450D DSLR with an Astrotech coma corrector. The latter is not a "full frame" camera, but still has a fairly wide field of view, and this coma corrector is unable to fully correct the whole field. Only the inner 1/3 or so is reasonably sharp, the outer parts show substantially enlarged, elongated, teardrop shaped images. Probably a combination of residual coma and field curvature.

I have not tried other coma correctors yet, I would like to try the newest Televue Paracorrs, but the cost of just trying them out can get fairly prohibitive. Given our similar sizes and speed instrument, I would be curious to see how the ones you mention work out over a wide field.

As far as photometry goes, I suspect the substantially different apparent star sizes would be detrimental to accuracy. One easy solution would be to offset the primary comp star and the target the same distance from the optical axis, giving the same distorted image pattern for both, though this adds some extra time and complexity to pointing on the objects, and is hard to use any more than a single comp star precisely.

Mike

We're using a 3" Paracorr on an f/4 95cm telescope and a 16803 4kx4k sensor.  I don't recall any image distortion at the field edges, so I suspect the Paracorr does field flattening as well as coma correction.  I'll re-inspect the images shortly.  I have a 3" Paracorr for my personal 80cm f/4 telescope, but it won't be installed for a few months.

The problem with the 16803 and the IMX455 (used in the QHY600 and ASI6200) is that these are big sensors that require large corrected fields.  The diagonal on the 16803 is 52mm, and that of the IMX455 is 43mm.  That means you have to use the larger 3" Paracorr, 50mm filters (the round ones will work with the IMX455), larger robust focusers, etc.  So while the CMOS sensors make for reasonably-priced cameras, you will still have a large budget for the ancillary stuff!

Arne

Regarding photometry with, say, coma.  You don't lose any light, so the comatic images contain just as much light as if they were perfectly round in the center of the field.  The issue is that most photometry software assumes a constant aperture size for all stars in a frame.  Therefore, if the effective fwhm is larger on the edges, then less of that total light gets included in the aperture and the edge stars will be systematically fainter than the center stars.

There are several ways to correct for this.  As mentioned above, you can use a field center that places the target and a comp star equally distant from the optical center.  In most cases, the distortion is axi-symmetric, so the differential photometry is correct.  You can focus the telescope so best focus is in a ring away from the optic axis.  That increases the usable field, but at the expense of sharp focus in the center.  We did this at USNO-FS, where the R/C telescopes have a curved focal plane in one direction, and the thinned CCD sensors had a bow in them in the other direction, so you could not get sharp focus over the field.  You can use large measuring apertures, so that you contain most of the comatic light.  The encircled flux asymptotically approaches truth, so the systematic difference between the target and edge star will approach a constant value.  You can map the sensor, finding out how much fainter the stars appear on the edges than at the center, and create a correction matrix that is applied to the photometry.  That is what APASS does.  You can psf-fit the image with a psf that changes with radius from the optical center.  Both DAOPHOT and PSFex can do this.

In addition, optical distortion such as coma usually comes with field distortion, so that you can't use linear plate coefficients and find the corner stars - they can be may arcsec from the expected position.  The correctors like Paracorr give good star images, but you will still have field distortion.  On APASS, the distortion is about 30 arcsec near the edge of the corrected field.  As long as you are finding stars by WCS, and that WCS has appropriate high-order terms, you can get good photometry.  If you use sensor X/Y position, then that will change on how well you center the field from night to night or whether a GEM flip takes place during a time series.

In general, it is better to do photometry on round stars!  Unless you really need the entire field, I'd reduce the size of the photometric region to those stars that are in good focus and ignore the rest.

Arne

Hello! Thank you all for your comments.

    I have one last question - How much larger might the FWHM of stars be at the edge of a full frame image compared to those at the center (after center focusing) because of uncorrected curvature of field after using an appropriate full frame coma corrector?

    I've looked at two Coma correctors -  3" Paracorr and 2.5" Riccardi Wynne. I believe that the Paracorr has some curvature of field correction. I am not sure about the Wynne. I will follow-up with both for additional information.

    My goal with this project is two-fold:

    1) Enjoyment of an ATM project. (To be frank, this is starting to lose its allure as I try to figure an f3 mirror!)

    2) Develop a system that has a large field so that I can image and then analyze multiple targets with a single exposure.

   With 2) above, I am not interested in imaging single targets in which the comps are widely separated and need such a large field, though I would likely participate in campaigns where such is needed.

    Similarly, I prefer to avoid cropping the field of a full frame sensor. Instead of doing that, I would use a smaller CCD/coma corrector than full frame.

    With MPO Canopus, I can create a file and perform photometry on all targets in a full frame image simultaneously. However, I cannot change the aperture for different targets in the same image during the run. I would prefer to use Canopus, if possible, rather than learning a new program, like DAOPHOT and PSFex, in order to use PSF fit the the radius of the image

    As Arne noted above, I can use a measuring aperture that includes all flux from each star from center to edge. However, Mark's calculations suggest that the star images at the edge (after center focusing) may have FWHMs that are too large to be overcome with a reasonable aperture for stars at both center and edge.

    Finally, I use SGPro which averages the FWHM from a number of stars. I don't know how stars are selected, but this may mean that the average FWHM for the image would be that for stars some fraction out from the center to the edge rather than at the center, so the required aperture would likely be smaller than if the image be focused for center sharpness.

    So, is there a way to estimate change of FWHM with defocus caused by curvature of field as star images go from center to edge in full frame images and what aperture might be needed that would be appropriate for star images at both center and edge of the image?

    I think this is the information I would need to see if residual curvature of field after using a coma corrector might be too severe over a full frame sensor with my 10" f3 design.

    Thank you and best regards.

Mike

PS: I had not thought of star image positions and plate solving with WCS vs. X:Y coordinates. I'll ask Brian with MPO Canopus how this is done. If the stars at the edge cannot be plate solved due to residual curvature of field effect and field distortion, then it would not matter how small a star's FWHM is at the edges of the image! Thank you for the guidance. MAH

Hello! I've taken a step backwards - some small grit broke off from teh bevel and scratched the mirror in several places during figuring. Oh well - lots of time during COVID lockdown!

    In any case, I asked for field curvature guidance at ATM forum in Cloudynights. It was suggested, as Mark did, that the star image blur would be 30 to 45 microns. If a coma corrector cut this in half, to abut 20 microns, then with 3.76 micron pixels of the IMX455 chip (and 3 to 4 arcsec seeing), the FWHM comes to about 6 to 7.

    If so then a single aperture should suffice across the image for aperture photometry of all targets.

    Do these numbers seem about right? Thank you.

Mike

Hi, Mike -- this is actually turning out to be a good exercise for me, because I'm also considering a short-focus Newtonian (12", f/4) but with a smaller sensor (monochrome IMX751 cropped to a total field width of 20 arcmin) for photometry.

So, yes, if you adjust focus to minimize the worst-case blur, the focal plane will be +/- 152 microns away from the plane of the sensor at the center and corners. At f/3, the blur diameter due to focus will be 50 microns. If the coma corrector fixes half of that, you have a blur diameter of 25 microns plus seeing of 3.5 arcsec. (Note that with this camera/scope, your pixel scale is almost exactly 1.0 arcsec/pixel, making some of this math particularly easy.) The blur diameter of 25 microns is a blur diameter of 6.7 pixels plus seeing of 3.5 pixels. In this case, I think they are pretty close to purely additive(?), so the total FWHM will be about 10 pixels.

General guidance is to use an aperture radius equal to double the FWHM, so aperture radius is 20 pixels (and aperture diameter is 40 pixels == 40 arcsec). I'm not sure that the general guidance is particularly applicable to this situation, so you may be able to use a smaller aperture radius?

Some thoughts:

• The secondary mirror's obstruction shadow will have a diameter of 1-2 pixels, and so should be pretty easily visible in the star images in the center and corners of the frame.
• The aperture diameter of 2/3 of an arcminute will be problematic in crowded fields. Star images will overlap (regardless of aperture diameter). But if you stick to photometry in sparse fields, you may be okay.
• You haven't talked about your photometric filters, but the f/3 light cone will require really large filters to cover the corners of the sensor.

- Mark M

Thanks! 20 pixels sounds too  much.

Mike

You have not mentioned the secondary mirror, if indeed you plan to use one for this design. The secondary will be rather large (depending on how low you can make the focuser), and you may need to deal with uneven illumination at the focal surface. Flat fielding corrects this, of course, but the larger the correction, the larger the errrors. A coaxial design design (i.e., prime focus camera) might actually give you a smaller obscuration and a more uniformly illuminated field. 
in an alternative universe, you could make a high-throughput system by combining four 8-inch f/5 mirror and smaller cameras to gain a multiplex advantage of shooting with multiple filters simulanteously. Probably about the same total cost. Use the 10" f/3 as a super deep-sky visual telescope as Mel Bartels does.

Thanks! I am planning a 4" secondary, which would give 40% obstruction.

    If this works out, my "ultimate" scope would be 18" f3  meniscus mirror 3/4" thick. That would give 1/2 the curvature of field as the 10" at the edge of the field. Of course, ATMers always dream big.

    Especially given the problems I've been having withe 10" f3 mirror, I might get to the 18" in 10 years! Best regards.

Mike

Hello! After much travail, I'm approaching last stages of mirror figuring for my 10" f3 mirror, which means going to Star Test. As such, I'll need to decide of how much field flattening occurs with TeleView ParaCorr.

    I would appreciate any real world guidance folks might have. Presuming a FWHM of 3 at center of field, how large might FWHM be at edges of field with -

   1) 2" Paracorr and APS-C chip using 3.76 micron pixels and 6300 x 4200 pixel chip (29mm diagonal)?

    2) 3" Paracorr and full sized chip using 3.76 micron pixels and 9600 x 6400 pixel chip (43mm diagonal)?

    I've asked the folks at Paracorr if they could run the spots for me, and they graciously agreed. If anyone has any real world experience, I would appreciate that for comparison. Best regards.

Mike