## Telescopes

www.lens-designs.com

**February 7, 2021 **** - ****8**** files posted from Braat & Török's ****Imaging Optics**

Joseph Braat kindly provided some detailed explanation of the designs:

"Example 7.40b is a classical Cassegrain telescope with parabolic primary (κ = -1) and hyperbolic secondary mirror (Imaging Optics, page 474, f =66.7 m, D=8 m, NA=0.06, angular field 2x19arcsec). The (curved) field of the telescope is limited by coma since the telescope does not satisfy the Abbe sine condition. The diffraction-limited field is limited to a diameter of 12.3 mm. For a wavelength of 550 nm, using the Rayleigh resolution criterion, we have that the number of resolved points NR on the diagonal is equal to 2200. Since the useful field is very restricted, its basic curvature is of no importance when a flat detector is used.

"Example 7.45 is an aplanatic Ritchey-Chrétien telescope (Imaging Optics, page 482, f =69.57 m, D=8 m, NA=0.0575, angular curved field 2x1.3arcmin), with an ‘almost’ parabolic mirror (κ = -1.08) and a hyperbolic secondary (κ = -4.9). Note that the aplanatism is valid up to the fourth order wavefront aberration since the conic constant values have been derived on the basis of third-order aberration theory. The useful diameter of the curved image field is limited to 52 mm by astigmatism and yields approximately 18000 Rayleigh-resolved points on the field diagonal. In the presence of a flat detector, the useful field diameter is reduced to 42 mm and the number of Rayleigh-resolved points NR is 14500.

"Example 7.46 is an anastigmatic Couder telescope (Imaging Optics, page 482). Specifications are f =20 m, D=8 m, NA=0.20, angular curved field of 2x5 arcmin, with a strongly hyperbolic primary mirror (κ = -8.2) and an elliptical secondary (κ = - 0.7) according to the fourth-order wave aberration theory. The useful diameter of the curved image field is practically zero due to a strong sixth-order spherical aberration residue. If we correct the system to higher order and eliminate the sixth-order spherical, the useful field diameter is limited to 200 mm by higher-order astigmatism and coma. In this case the number of Rayleigh-resolved image points NR would amount to 200000 (λ =550 nm).

"Example 7.49a is an aplanatic Cassegrain telescope (Imaging Optics, page 487), designed with the aid of Schwarzschild’s analytic method to obtain the shape of the general aspheric surfaces in a point-by-point way (Imaging Optics, page 487, f =7.25 m, D=8 m, NA=0.55, angular curved field 2 x 1arcmin). The number of Rayleigh-resolved image points NR on the field diagonal is 6600.

"Example 7.49b is the Couder telescope (Imaging Optics, page 487), `aplanatically’ designed with the aid of Schwarzschild’s analytic method (see subsection 7.6.6 of Imaging Optics) to obtain the shape of the general aspheric surfaces in a point-by-point way. Specifications: f =4.444 m, D=8 m, NA=0.90, angular curved field is 2x1.5 arcmin). The number of Rayleigh-resolved image points NR on the field diagonal of 4 mm is approximately 11000 (λ =550 nm). We remind that the Couder telescope, despite its theoretical superiority with respect to aberration over the Cassegrain telescope, has not effectively been used in astronomy. The reason is that a number of practical inconveniences are found in this telescope design such as an unfavourably large obscuration ratio, difficult access to the image space and a high aperture value at the detector side.

"Example 7.55a is a three-mirror anastigmatic telescope according to Paul (Imaging Optics, page 492, design proposed in 1935), scaled to an entrance pupil diameter of 39 m, in line with the specification of the European Extremely Large Telescope (ELT). The specifications are f =50 m, D=39 m, NA=0.39, construction length 0.9D, angular field 2x9.6arcmin (λ =550 nm). Within the field extent corresponding to diffraction-limited imaging, the field can be considered to be flat. The number of Rayleigh-resolved image points NR on the field diagonal of 280 mm is approximately 325000 (=550 nm).

"Example 7.55b is a three-mirror anastigmatic telescope according to Paul-Baker (Imaging Optics, page 492, design proposed in 1969), scaled to an entrance pupil diameter of 39 m, in line with the specification of the European Extremely Large Telescope (ELT), with f =75 m, D=39 m, NA=0.26, =550 nm, construction length 1.4D, angular (flat) field 2x11 arcmin. The number of Rayleigh-resolved image points NR on the field diagonal of 280 mm is approximately 372000 (λ =550 nm). Compared to the Paul anastigmatic telescope, the Paul-Baker design leads on the one hand to an increase of the construction length but provides easier access to the image plane and facilitates the insertion of auxiliary optics. There is also the advantage of a smaller image-side aperture of the focusing beams. The residual aberration in the field is also more uniform than in the Paul-design. "

**November 10, 2019**** - 65 files posted from Handbook of Optics**

Making models from the prescription in the Handbook was straightforward. The prescriptions generally are scaled to an entrance pupil diameter of 200mm, and generally shown with only an axial field point. For the sake of continuity, I generally built the models with the same field of view. I suspect that this field of view is wrong for all reasonable applications. I also ignored obscurations.

**January 24, 2017**** - Four files posted**

These files are mostly of unobscured all-reflective designs. This class of designs is interesting because it generally takes full advantage of modern methods for making aspheric optics. I've never worked with such systems, but the look like they'd be lightweight and compact. Unfortunately, complex coordinate transformations are necessary to define the system clearly, complicating the task of building models from the patent disclosures.

**August 15, 2018**** - 17 Gabor variants posted**

David Shafer’s recent article in Optical Engineering contains many schematics of what’s come be known as the Gabor design. He cautions that many of these designs are not especially useful as they stand, because of a curved image and poor color correction. Instead, they are generally meant to illustrate three points:

1) Even simple designs can have multiple solution regions and those should be explored.

2) Very high performance with very simple designs can be achieved if a curved image is allowed, and

3) Good starting points for further complexity can be generating by a solid understanding of aberration theory and prior design history

Furthermore, I’d like to note that this set of models is further evidence that the prescriptions contained in patent literature can be misleading. Gabor’s British patent (#544,694A) is not well corrected, and optimum performance places the stop far from the concentric position as described in Shafer’s paper. The model is included here anyway; it’s fun to re-optimize such classic designs, pretending to be a better designer than the people from long ago.

I needed help to generate some of these models. I was able to generate models that looked very much like the figures, but straightforward optimization drove the system to other solutions, with much worse performance that David describes in his paper. David kindly helped me, though, sending several complete prescriptions. More importantly, he helped with some insight. Some of the designs balance large aberrations across surfaces; this balancing is likely to give local minima in merit functions. Figure 6 in the paper is an example of such a system.

Let me close by noting what a tremendous resource David Shafer has been. He’s helped a lot with generating of these models. More importantly, he has a long history of instructive and thought-provoking publications, many of which are summarized on his slideshare (https://www.slideshare.net/operacrazy) account. I’ve always enjoyed reading his work; after this exercise, I can attest that his papers all deserve detailed study, by building models or working through the aberration theory.

**Summary of designs**

**Design files**