In the 1960 S Large Telescopes That Could Be Purchased Were 8-10 in Diameter

Optics - The Series

Using the Moon to Quantify Achieved Telescope Resolution

Shane Santi – President

Dream Telescopes & Accessories, Inc.

Copyright 2017 – v3

Star testing a telescope is a traditional method for qualitatively testing the performance of an assembled telescope. Dream recently finished a 16” f2 IR telescope (see Fig. 1) that required the 2-mirror portion of the system to be tested independent of the 6-lens IR relay. NASA LRO images of the Moon were used to quantify the resolution the telescope achieved.

Fig. 1: 16” telescope SW CAD model & actual telescope mounted for real-sky testing.

Both M1 and M2 were independently tested in finishing but a system test is always valid because it accounts for all aspects of the telescope, like; impact of mirror mounts, optical alignment of the two mirrors, performance loss due to spacing of M1 to M2 that is out of tolerance, flexure of all components, focus shifts, etc.

The 2-mirror system was a Classical Cassegrain with a focal ratio of f6.5. The 2-mirror’s inherent focal plane was roughly 1/3rd of the way back toward M2, not behind M1 like a conventional Cassegrain. This arrangement and space limitation in this area forced the use of a smaller test camera for under-the-sky testing. The camera’s detector was 3.6mm x 4.8mm with 3.75µ pixels. The pixel size in combination with the 16” f6.5 2-mirror system yielded 0.3 arc-seconds/pixel. The detector’s peak sensitivity is centered on 550nm wavelength. No filter was used during testing and no processing was done to the images after.

Because the camera was small and very light, only 45 grams, a simple mount inside the carbon fiber M1 conical baffle was used to hold the camera. This allowed the ability to align the camera and to hold that camera at the correct axial position, providing the X, Y & Z positioning needed. In testing, optimal focus was achieved with only a 0.018” inward movement of the motorized M2 from the nominal spacing position of M1 to M2. It is important to keep the spacing of M1 to M2 within an optimal window because going outside this tolerance will initially lead to increased off-axis aberrations (performance loss at the edges of the field), but will eventually lead to on-axis degradation as well (on and off-axis performance loss).

Fig. 2: Simulated (left image) and actual (right) Field Of View

using test camera with 16” f6.5 telescope.

The horizontal rectangle frame shown near the center of the Moon in the left image in Fig. 2 shows a simulated Field Of View (FOV) of the camera/telescope, with the actual image shown to the right.

Fig. 3: LRO image of FOV (left) and actual test image from 16” telescope (right).

The left image in Fig. 3 was taken by a NASA probe orbiting and mapping the Moon; LRO. The image was taken from the LRO public web site here: http://target.lroc.asu.edu/q3/ .

Fig. 4: Closer and closer LRO views of the target area for determining actual resolution.

Fig. 4 shows closer LRO views of the target crater used to determine resolution of the telescope. The left image in Fig. 5 is an LRO view with a lunar scale, which is easier to see in Fig. 6. The scale in the left image of Fig. 5 shows 5km on the top and 2mi on the bottom of the scale. The right image in Fig. 5 is the actual, single test image taken with the camera and 16” f6.5 telescope.

Fig. 5: LRO image (left) and actual test image (right) from 16” telescope: not shown in the same scale.

Fig. 6 shows the closest view possible with LRO images at the time of this writing. This shows the crater used to help quantify the resolution of the telescope is roughly 2km in diameter. But the test image shows both light and dark within this diameter. Conservatively this image has achieved lunar surface resolution of roughly 1.5km.

This lunar surface resolution can be converted into arc-second resolution from Earth. 0.3 arc-sec/pixel for the camera equates to 0.51-0.59km on the Moon. The km variation is caused by the exact distance to the Moon. 1.5km lunar surface resolution achieved in the test image is 2.727 times greater than what 0.3 arc-sec/pixel equates to on the Moon (1.5km / 0.55km = 2.727). To determine the achieved arc-second resolution of the telescope we take 2.727 times 0.3 arc-sec. The resolution achieved by the telescope is roughly 0.818 arc-second.

The spacing of M1 to M2 was mentioned earlier because it is one of many factors that influences performance of the optical set, beyond the quality of the optical surfaces themselves. Another aspect to performance is related to the radius tolerance for each mirror. Going outside a given system’s tolerance will increase aberrations. The radius tolerance for each mirror of this IR telescope was +/-0.1%. Using this tolerance M1’s radius could be 2413.0mm, +/-2.4mm, while M2’s radius could be 1143mm, +/-1.1mm. M1’s finished radius was only 0.218mm or 0.009% long (2413.218mm actual). M2’s finished radius was only 0.008mm (8µ) or 0.0007% long (1143.008mm actual).

Fig. 6: LRO image with lunar scale showing target crater’s diameter.

To achieve higher resolution, without moving the telescope to a pristine mountaintop, a UV filter could be used. Using a camera with a smaller pixel pitch is another potential option. Stacking hundreds to thousands of the best images would also improve the overall image(s) as well. This was not done because as soon as processing of images is allowed into testing, the results should always be viewed as tainted. The goal was to show the raw performance of the telescope. Processed images can show unrealistic performance and they strip away the ability to maintain an apples to apples comparison. A telescope that offers better raw images will always beat one that needs processing to achieve “quality.”

To see a video of 254 consecutive 0.012 second images highlighting the movement and distortions that our atmosphere causes, click here.

The seeing in the video is atmospheric, not mirror-seeing, because both mirrors were Dream's zeroDELTA™ engineered lightweight mirrors and the low-mass, high-stiffness and athermal carbon fiber telescope used Dream’s FAST™; Dream’s Filtered Air System Technology. FAST™ fills the telescope chamber with filtered/clean air, as well as helping to maintain an extremely low temperature delta between all components inside the telescope and the outside ambient air. It also greatly reduces the number of cleanings required, which both helps to maintain reflectivity at higher levels and reduces the number of re-coatings needed. As with all athermal Dream telescopes 95% of the telescope structure weight is carbon fiber with only 5% being conventional metals.

The Dream zeroDELTA™ primary mirror, shown in Fig. 7, was a 16.5” physical OD, 2.5” tall and weighed just 9.5 pounds. The thickest features of M1 were 1/8”, causing the mirror to equalize exceedingly fast, allowing optimal performance.

Fig. 7: Dream’s zeroDELTA™ lightweight mirrors and carbon fiber telescope.

The thin faces used on Dream’s zeroDELTA™ lightweight mirrors have numerous advantages;

· Shorter Thermal Time Constant: equalize to ambient temperature faster.

o Little to no internal temperature gradients to warp the mirrors’ figures.

o Little to no boundary layer degradation.

· Lower self-weight deflection: mechanical figure distortion.

· Moves the CG of the mirror farther behind the optical face, which has many benefits.

· A lighter mirror means it is easier to hold tighter opto-mechanical tolerances.

· It makes the telescope lighter; faster slews, more accurate pointing and tracking, etc.

This author has been studying lightweight mirrors for the past 25 years, as well as designing and using them for the past 15 years. Modern engineering tools are used to analyze the designs for both polishing displacement (print through) and different gravity cases (actual mirror mount & final use).

Below is high resolution interferometry data from this telescope’s primary mirror, which was finished in-house. The data shows how little Mid-Spatial Frequency (MSF, historically called primary ripple) errors are in this Dream zeroDELTA™ engineered lightweight mirror. The band number is defined toward the top of the graphic, giving a description of the physical size of MSF error being evaluated in that column.

Fig. 8: Dream’s zeroDELTA™ 415mm, f3 concave paraboloid.

The zeroDELTA™ primary mirror had a face of roughly 0.1" thick. This is a superb example of why Dream’s real and extensive engineering, to optimized the zeroDELTA™ mirrors to historically unprecedented levels, matters. The mirror can have all of the mechanical and thermal benefits that come with this level of lightweight mirror but have the finish normally associated only with solid mirrors. The mirror was processed using a conventional over-arm machine and pitch-based polishing.

Conclusion –

In 1928 G.W. Ritchey wrote, “We shall look back and see how inefficient, how primitive it was to work with thick, solid mirrors, obsolete mirror-curves, ...”1

Ritchey discussed numerous “refinements” in optics and mechanics that each could improve the performance of the telescope. His critics often claimed his “refinements were too technical, and especially too laborious” 2 to be practical. Yet he consistently used a 0.5m telescope that out-resolved much larger telescopes of the time. The Cassegrain design that he postulated is still the highest performing 2-mirror design ever developed.

What some may view as their site-seeing limit may in fact be their current mirror-seeing and/or mechanical errors limit. Considering this 16” Dream telescope was tested at just below 500’ elevation, in the center of a ~6000 person town that sits 75 miles west of NYC and 75 miles north of Philadelphia, the sub-arc-second resolution achieved is superb. Especially when one considers that this is a single image, not a stack of hundreds to thousands of images, and that no image sharpening or processing has been done. This is the raw performance of the telescope.

1 The Journal Of The Royal Astronomical Society Of Canada, Vol. XXII, No. 9, November 1928.

http://adsabs.harvard.edu/full/1928JRASC..22..359R

2 The Journal Of The Royal Astronomical Society Of Canada, Vol. XXII, No. 6, July-August 1928.

http://adsabs.harvard.edu/full/1928JRASC..22..207R