TOA-150/KAF-09000 design study

November 16, 2013

This note explores the use of a Takahashi TOA-150 refractor and a TrueSense KAF-09000 sensor as a higher resolution imaging alternative to my current FSQ-106EDX and KAF-8300 setup for ionized hydrogen region photography.


The resolution of my current setup is pixel size limited. With my recent changes to eliminate sensor tilt and temperature dependent focus drift, the star full width at half maximum (FWHM) measurements are slightly less than one pixel in good seeing conditions. My setup has a 4.2 arcseconds per pixel image scale and can consistently achieve a FWHM on 40 minute subframes of about 4 arcseconds in good seeing conditions.


It would be possible to double the resolution of my setup by binning the KAF-8300 sensor 1 x 1 rather than 2 x 2, but, for any fixed exposure time, doing so would decrease pixel signal-to-noise ratios (SNR) by a factor of 2 or more, depending on the brightness of the target with respect to the sky background and camera noise. This loss of SNR would penalize image quality in the dimmer areas of my photographs. In my experience, surfacing dim nebula structures requires good SNR. The large increase in exposure time required to mitigate this loss of SNR is not practical for a mobile setup.


To double resolution and maintain SNR with the same exposure length and the KAF-8300 binned 2 x 2 would require an aperture of 212 mm and a focal length of 1060 mm. A refractor with such dimensions is not available. Reflector telescopes with similar dimensions are available, but I prefer a refractor for image quality and ease of use reasons.


The Takahashi TOA-150 with the TOA-67 field flattener offers an aperture of 150 mm and a focal length of 1090 mm. Such a setup with the KAF-8300 binned 2 x 2 would offer double the resolution but a slower speed and half the field of view. As an alternative sensor, the KAF-09000 offers a larger pixel size and a higher quantum efficiency, both of which would offset the loss of speed. The larger pixel size of course would decrease resolution slightly. The larger sensor size increases the field of view.


The TOA-150 is well regarded due to its extremely high image quality. It satisfies the Thomas Back modern definition of Apochromatism. The TOA-150 offers dual use, visual and photographic. TOA-150 optical evaluation.


blog 2013_11_15 TOA objectiveblog 2013_11_15 TOA objective


blog 2013_11_15 Flattenerblog 2013_11_15 Flattener


The diagrams below show the on-axis and off-axis spot sizes for the FSQ-106EDX and the TOA-150. The KAF-8300 sensor has a half width of 9.0 mm and a half diagonal of 11.2 mm. The KAF-09000 sensor has a half width of 18.3 mm and a half diagonal of 25.9 mm. The 22 mm off-axis spot of the TOA-150 is smaller than the 11 mm off-axis spot of the FSQ-106EDX. It appears that spot sizes across a TOA-150/KAF-09000 frame will be no larger than those across a FSQ-106EDX/KAF-8300 frame. In practice, collimation, focus, seeing and guiding will likely be the dominate factors in achieved star size, i.e., FWHM.


blog 2013_11_15 FSQ spotblog 2013_11_15 FSQ spot


blog 2013_11_15 TOA spotblog 2013_11_15 TOA spot


The table below shows image scale, field of view, and relative SNR metrics for the two setups. My formulation of the SNR metrics is explained here. For this comparison, exposures time is 40 minutes, camera noise statistics are based on my measurements for the KAF-8300 and values from FLI for the KAF-09000. The higher efficiency of the TOA-150 setup is due to the higher quantum efficiency of the KAF-09000. The slower focal ratio of the TOA-150 is not completely mitigated by the larger pixel size and higher quantum efficiency of the KAF-09000, its photon noise limited SNR remains slightly less than the FSQ-106EDX. On the other hand, the background noise limited SNRs are similar. This is primarily due to the fact that the read noise of the KAF-09000 when binned 1 x 1 is less than that of the KAF-8300 when binned 2 x 2.


The field of views of the two setups are nearly the same. Image scale of the TOA-150 is almost half that of the FSQ-106EDX. When combined with the KAF-09000, the TOA-150 will provide nearly twice the resolution at the cost of a small loss in SNR performance, assuming 2 arcsecond or smaller seeing. To match the photon noise limited SNR an exposure time about 36% longer is required. Such a longer exposure would also result in a better background noise limited SNR.


Telescope Sensor Aperture Focal length Pixel size Efficiency Image scale Field of view Photon noise limited SNR Background noise limited SNR
FSQ-106EDX KAF-8300 106 530 10.8μ 40% 4.2"/p 1.7° 1.4 0.09
TOA-150 KAF-09000 150 1090 12.0μ 51% 2.3"/p 1.9° 1.2 0.09


Unfortunately I do not have measurements of seeing at my usual mobile observing sites. For my next observing sessions, I plan on making short exposures with my current setup binned 1 x 1 at an image scale of 2.1 arcseconds per pixel. I am also hoping to experiment with other seeing measurement techniques. FWHM measurements will help me judge how often a 2 arcsecond or smaller seeing occurs, and how often pixel size limited FWHM subframes might be achieved.
The KAF-09000 can be binned 2 x 2 for below average seeing conditions. The table below shows metrics for this setup, with dark current increased by a factor of 4, and read noise a factor of 1.5. Assuming there are no adverse issues with binning (e.g., significant blooming), such a setup would combine a resolution nearly equal to my current setup with a nearly doubled SNR.
Telescope Sensor Aperture Focal length Pixel size Efficiency Image scale Field of view Photon noise limited SNR Background noise limited SNR
TOA-150 KAF-09000 150 1090 24.0μ 51% 4.5"/p 1.9° 2.4 0.19

The TOA-150's critical focus zone (CFZ) at f/7.3 is about twice as wide as the FSQ-106EDX at f/5. However, the TOA-150 optical tube assembly (OTA) is twice as long. I speculate that the temperature change sufficient to move the focus plane by one CFZ width is roughly the same on both setups. The TOA-150 design uses large air spaces between elements, these can take time to reach equilibrium with a significant temperature drop. The focus drift temperature dependency of the TOA-150 may be more difficult to model than the FSQ-106EDX for a mobile setup exposed to varying weather conditions. Good modeling is necessary for accurate temperature dependent focus drift compensation.


The KAF-09000 is known to have a large residual bulk image (RBI) problem. On targets with relatively dim nebula, saturated star RBI will be the primary problem. Randomized dither patterns are a known workaround for saturated star RBI, as long as the dither radius is larger than the saturated star diameter. After subframe alignment, star RBI echos are randomly positioned around the star's actual position, and will be removed during integration by standard rejection techniques. Bright nebula RBI remains a problem, and cannot be removed similarly with any reasonably sized dither radius. Warming the camera and then recooling it between every exposure is an alternative solution, at the price of a time penalty. The FLI ML09000 camera has an advertised cool down time of 5 minutes. Such an overhead may be acceptable given that it is small compared to the expected 40 to 60 minute subframe exposure time, for those occasional targets with extremely bright nebula.


blog 2013_11_15 FLIblog 2013_11_15 FLI


The weight and length of the TOA-150 are twice that of the FSQ-106EDX, which will place increased demands on mount stability. The higher resolution will place increased demands on guiding accuracy. My experience has shown that if root-mean-square (RMS) guiding error is no larger than 25% of achieved FWHM then the negative impact of guiding errors is negligible. My current mount has no trouble achieving an RMS guiding error of less than 1 arcsecond in almost all conditions, which meets the 25% requirement for my setup. The TOA-150/KAF-09000 will required no more than 0.6 arcsecond RMS guiding error. My current mount can achieve this requirement occasionally in excellent seeing conditions, with a payload half the weight of the TOA-150 setup. The mount will likely need to be upgraded, possibly to one with encoders that eliminates nearly all gear train periodic error and hysteresis.


An imaging train setup will require an off-axis guider and a filter wheel between the field flattener and camera. If sensor detilting is required, a detilter device will also be needed. There appears to be sufficient flattener backfocus for all of this. Detilting behind the flattener however will be tricky because of the strict flattener backfocus requirement, and I am not sure such detilting is feasible because of this. Placing a detilter in front of the flattener may be a better alternative, however existing detilters don't appear to have enough internal clearance to avoid vignetting when mounted so far from the camera. Shimming the camera or using one with internal tilt adjustments may be the only alternatives. The TOA-150 manual focuser can be replaced with a digital focuser easily.


Collimation of the TOA-150 may be straightforward, but I have seen the instructions in Japanese and not English. There are two sets of three collimation screws, each with a pair of locking screws, that appears to enable lens element tip/tilt and possibly spacing adjustments. The collimation procedure appears to rely on collimation telescope images, out-of-focus star airy ring shapes, and a Ronchi test. The FSQ-106EDX, on the other hand, can not be collimated by the end-user, due to its complex, modified Petzval, four-element optical design.


The KAF-8300 suffers from blooming when binned 2 x 2, due to the limited well depth of its output registers. In my current setup's subframes the blooms are restricted to stars brighter than about 10th magnitude, are small, and are not an image quality issue in the final photographs in my opinion. The KAF-09000 when binned 1 x 1 likely has no blooming issues. The full well depth of the KAF-09000 when binned 1 x 1 is about twice that of the KAF-8300 when binned 2 x 2.


I measure about 5% vignetting at the corners of a subframe from my current setup. The TOA-150 is claimed to be fully illuminated to a 30 mm radius, so vignetting should not be an issue for the proposed system. Photo response non-uniformity (PRNU) is not specified by TrueSense for the KAF-8300. I estimate PRNU is less then 0.5% when binned 2 x 2. PRNU of the KAF-09000 is specified at 0.5%. Panel flats work very well for my current setup, and I expect they will work likewise for the proposed system.

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