Some telescope designs. Due to space limitations, many of these are only in OSLO .len format prescriptions.

I was always curious about the Cooke triplet. James G. Baker has an article in the ATM series that describes a pair of such triplets. Here is my modification. It is designed against the visual (photopic) range, similar to his 5461 A version. I also wanted to call this: What are you going to do with that slab of BK7?

What can one do to improve the bandwidth of a Schmidt-Cassegrain. I adapted this design after a design in Rutten and Van ven Venrooij, but used an achromatic corrector plate.

The Companar Maksutov Cassegrain has good performance. I added a small corrector lens, attempting to flatten the field. Not too successful, but the performance here seems reasonable, if you ignore the fact that you have six air-glass surfaces.

Here are a couple of APO designs from Steve Fejes. The first has all spherical surfaces, while the second has an aspheric (oblate, unfortunately) surface. I think these two point out the possibilities available when judiciously using air-spacing.

Steve and I combined for this next example of a slow refractor. In this case, however, the introduction of an air space moved the correction slightly toward the blue, pulling a third null well into the photopic region. The curves here are relatively steep for f/20, due to the narrow range of Abbe numbers in the glasses. It may also be difficult to obtain BaLF5 or N-BaLF5 stock. If this could be overcome, the glasses selected here are relatively cheap.

When I started attempting to design APOs, I wanted to learn about the the variations in ED glasses. I ended up with a series of telescopes that provided a little study that included several of these glasses, but with the other lenses in common. I reoptimized the S-FPL51 version to use BK7 instead of K5. The performance was slightly better. This telescope differs in that the focus is achieved by moving the field corrector lens. The amount of motion is small to focus down to 50-100 m (about 6 mm IIRC). The intent here was to put the field corrector within the draw tube (there is not a whole lot of BFL).

This telescope has very wide band monochromatic correction. At f/12, it is not extremely fast and has some residual lateral color. At first, I thought this design was not even an achromat, as the longitudinal color across the visual had a definite slope. The maximum focus is actually at around 14000 A.

This telescope has a little better lateral color correction over the i-t band. Performance is about midway between the telescope above and the one with FPL-53 below.

The i-line catalog is invaded to come up with this telescope. This telescope is lambda/4 P-V from 334 to 2162 nm.

Here is another version of this telescope. This version does not have quite the same bandwidth, but has better off axis correction over the photographic band (3650 A to 7000 A) for a 90 mm field.

If this telescope is sped up, an adjustment of the glass types and thickness is needed. This version is at f/8, but is still optimized over the same physical field sizes (31.4 mm CCD, 50.4 mm visual and 90 mm photographic).

If the geometry of these five lens solutions is unacceptable, by reducing the stringent requirement for a really flat field, more acceptable geometries can result. In this solution, the field curvature is still low, with a radius about 1.5 times the focal length.

This design may also be implemented with a doublet front end. Here the correction does not extend as deeply into the blue. The photopic Strehl ratio is still 0.98 over a 44 mm field, though.

By reversing the field lenses, an even better geometry can result, with only a small loss. The tolerances on this telescope also appear to be looser.

One of the thing I dislike when reading optics books is it seems that the best refractor designs are made with glasses such as KzFS1 or TiF2. Did you ever try to find these? This f/20 design should consist of reasonably current glasses (at least for the next 12 hours).

Here is a version of the Ross Null Test in which the compensating lens has radii that are equal to the radius of curvature at the edge of an f/4 paraboloid. The theory here is that, when making the mirror, the lens can be figured against the mirror while it is still a sphere. Note the high dependence on the wavelength that comes from inserting the single element lens in the path.

The Wynne Corrector for a Newtonian provides reasonable performance on a flat field with good bandwidth. Here is an instance of it. The large space between the second and third lenses is utilized here to traverse the distance from the Newtonian secondary. The secondary itself is only indicated here due the 10 surface OSLO LT limitation.

Another example of the Wynne corrector but with 4 lenses (1 doublet, using a mild Fluorcrown, S-FPL51). This design was pushed to reduce the overall length of the corrector. Still, it produces somewhat reasonable spot sizes.

Glasses available elsewhere may not necessarily match those available here. I have used the ZEMAX nd/vd offsets to attempt to match some glasses available in India. I have modelled a borosilicate crown (1.5165/64.2) with BK7 and three flint elements: DF 1.617/36.6 with F4, DF 1.623/36.0 with F13, and EDF 1.648/33.8 with SF2 to produce three f/15 100 mm aperture designs.

Here is a design from Dan Chaffee that is his choice for a simple BK7/F2 doublet planetary f/18 scope. He has chosen here to provide low spherical aberration at the e line (5461 A).

Here is an f/15 triplet design using a special short flint (kzfsn4). F-C correction is about 1 part in 7000.

Here is an f/15 triplet design using an ED glass (s-fpl51). F-C correction is about 1 part in 14000.

Here is an f/15 doublet design using an ED glass (s-fpl51). F-C correction is about 1 part in 6000. The spacing here is designed to keep the last surface flat.

This is an f/6 design using an ED glass (s-fpl52 and s-fpl51). It is modelled after a Petzval design, but uses triplets, protecting these sensitive fluorcrowns.

This is an f/8 design also using an ED glass (s-fpl52 and s-fpl53), again using triplets.

This is an f/6.4 design, again using an ED glass (s-fpl53 and s-fpl52) in doublet configuration. A field flattener is added, giving a flat field over 6x7 format.

A family of visual triplets, all optimized against a photopic bandwidth:

        f/8     f/9     f/10     f/11     f/12

The same family, but modifying the thicknesses to make the off-axis centroid have minimal lateral color:

        f/8     f/9     f/10     f/11     f/12

The same family, but optimized within the field, i.e. the photopic Strehl ratio at the edge of the field is 0.8:

        f/8     f/9     f/10     f/11     f/12

Close to the above is this triplet. The advantage here is that the air space is gone, providing a low-cost (for ED, anyway) triplet.

        f/8     f/9     f/10     f/11     f/12

Depending, I think, upon the exact field and optimization goals, allowing an airspace in the above has the effect of equalizing the radii of the two inner surfaces. Here is an example, where these inner radii are chosen to be exact values.

I parametrized a version of the above (with alternate glass selection) on the ROC of the ED lens. Using the glasses C3, FCD1, and S-BSL7, where the FCD1 lens has a clear aperture A, an ROC R, and an edge thickness E (at the clear aperture diameter), a lens with f-number f is provided by the equations:

    c = A / R
    d = c - 0.4
    e = E / A
    g = e - 0.05

where:

    f*c = 4.2202 - 0.075*d - 0.1805*d² + 0.013*g
    R1/R = 2.22737 - 0.0353*d - 0.05333*d² - 0.38594*d³ + 0.027*g
    R5/R = -11.58735 + 0.51585*d + 2.08978*d² - 8.05035*d³ - 0.69*g
    T3/R = 0.0020238 - 0.0007235*d - 0.001397*d² - 0.000335*g
    T1/A = 0.07
    T5/A = 0.07

This seems to provide reasonable systems near the nominal edge thickness for values of c in the 0.25 to 0.55 range. This covers the f/8 to f/16 range. I provided an example of this, where the ROC and thickness of the ED lens were selected for convenience.

A variation of this, using the three Hoya glasses BSC7, FCD1, and E-C3, eliminates the airspace. Letting v be the inverse of the focal ratio and F be the focal length, the four lens radii of curvature are given by:

    R1/F = 0.528424 - 0.023967*v + 0.151458*v² - 0.211893*v³
    R2/F = 0.214038 - 0.019676*v + 0.250189*v² + 0.089862*v³
    R3/F = -0.291430 + 0.010787*v - 0.003571*v² + 0.065833*v³
    R4/F = -2.765991 - 0.324750*v + 3.515658*v² - 4.837847*v³

In this case both T1/A and T3/A are as above (0.07), while E/A is fixed at 0.04, after allowing for a diameter 8 percent larger than the clear aperture. The back focal length, BF, and image radius of curvature, RI, are given by:

    BF/F = 1.000056 - 0.108936*v - 0.663958*v² - 0.317951*v³
    RI/F = -0.371113 - 0.028800*v - 0.202718*v² + 0.066379*v³

For a 150 mm aperture, this design is photopically above the diffraction limit across a 24 mm diameter image at f/8.5, as shown in this example.

This same glass combination, can be reoptimized against a field corrector.

Here is a triplet-doublet design. The removal of the airspace seemed to require that field flatness not be a design parameter. Note that spherochromatism is not fully corrected, opting instead for field coverage.

        f/6.4     f/8     f/10     f/12.5     f/15.6

Looking another way, the following spans a range of 4-9 inches of aperture, decreasing speed with larger aperture, ranging from f/6 to f/8, so that performance is roughly the same.

        4 in f/6     5 in f/6.4     6 in f/6.8     7 in f/7.2     8 in f/7.6     9 in f/8

Here is a small apochromatic double Gauss camera. (Sorry, no OSLO file -- a double Gauss will not fit within the limits set by OSLO LT.)

This is a small (100 mm aperture common glass (BaK2, LLF1) f/15 achromat. Although the F-C difference is large, the correction of aberrations seems poor, but the photopic Strehl ratio is still between .83 and .84 over a 21 mm field. Go figure.

This doublet came out of initial testing of the G-sum calculator.

Here are a couple of other doublets that came from the G-sum calculator. One uses S-BAM12, while the other uses KzFN1. The correction in the KzFN1 doublet may be a little too red for some. This can be corrected by moving the reference wavelengths; in this case, using 0.536 microns for the minimum focus wavelength and 0.560 microns for the central wavelength gives this solution.

When the system is not pushed for speed, some pretty good performance can be had. A bonus of this doublet is that performance is good out to better than 1 micron.

This doublet has good longitudinal correction in the visual. The Strehl is 0.925 Photopically.

Back-up plans, since K11 may be difficult to acquire. Red and blue, but neither has the balance of the original.

Or, plan C is, in some respects, better than the original, but still lacks the Photopic symmetry.

Deemphasizing off-axis correction can dramaticly change the on-axis performance. This 200 mm f/8 quadruplet has three lambda/45 P-V nulls in the active photopic region. In addition, color corrector is excellent at one part in 29,200 over the F-C region.

Now this cannot be cheap or somebody would have thought of it a long time ago! (Note: I found out later that MgF2 is bi-refringent!)

This 200 mm f/8 has some interesting features.

This 116 mm f/15 design seems to me to be most peculiar. It has no air spaces, but seems to have good performance well into the IR region.

The optimization technique suggested in my software page was used to transform one of Roger Cerrioli's designs into another. Using a flat spectrum from 410 to 730 nm, that design was morphed back to a form quite close to the original.

Two examples of a triplet (with a split field corrector) are given. Each is 150 f/8 with a fixed BFL of 225 mm, allowing adequate space for instrumentation. The first is optimized for photopic (visual) use, while the second is optimized for photographic (blue) use. The CCD version requires a bit more BFL, but is actually shorter.

Visually, if slowed back down to f/12, however, one of the lenses may be discarded altogether. Two additional examples are given. The first uses only Schott F2 glass. The second uses SF2 for the smaller lens, and is thus marginally more expensive, but provides a better fit.

Even better, this f/12, using the same F2/SF2 combination with a slightly different Lanthanum glass, S-LAH66. This glass is a somewhat more expensive than S-LAM60, though (3.6 vs 2.3 times the baseline price).

Given the steepness of the internal curve, I found it surprising that this lens can still be pushed down to f/8 (adjusting the size to fit stock S-LAH66 widths and returning to F2 as the last lens). The middle element gets a bit thick, however.

When the triplet form is reintroduced, performance is, however, dramatically improved. (Yes, I finally got a copy of the Hoya catalog -- hence the glass changes.)

Examining a few of these, it appeared as if the correction of spherical aberration was good for the upper visual and IR, but degraded significantly at wavelengths shorter than the g line (435 nm). If this is the case, the best that could be attained would be strong color correction in the IR, but with a tail-off in the UV that matched the worsening correction of spherical aberration. This version appears to be close to that. The spot diameter is 19.4 microns over the 365-1015 nm region, and 15.9 microns over the 365-700 nm region, while the Photopic Strehl is 0.999.

There may be a tradeoff here between residual field curvature and speed. In this 150 mm f/6 telescope, the P-V wavefront error is better than lambda/4.4 for the entire visual range (400-750 nm).

Here is another example.

The Cauchy and Sellmeier refractive index formulas are thought of as providing reasonably close answers. However, I found a Sellmeier formula for the refractive index of Hoya FCD1 glass, using the 5 digit index values provided by Hoya:

      B1 = 1.21054978
      B2 = 0.00790830392
      B3 = 1.66735095
      C1 = 0.0074229044
      C2 = -0.116766903
      C3 = 280.039749

while the Cauchy formula used by ZEMAX is given by:

      Am8 = -5.8852269E-7
      Am6 = 8.5142186E-6
      Am4 = 6.5046523E-5
      Am2 = 8.3470679E-3
      A0 = 2.2181132
      A2 = -5.799427E-3

The maximum difference between these two formulas for any of the Hoya supplied wavelengths is 4.32E-6 at the h-line, with the rest being less than about half that error. I optimized two designs, one using the ZEMAX supplied Cauchy formula, and the other using the Sellmeier formula I found. The prescriptions are somewhat different, but the RMS wavefront error over the i-t band differs by about 30 percent!

In the ATM books, James Baker suggests that CaF2, sandwiched between two crown glasses, may be utilized as the center element of a Cooke triplet. Here is my attempt at finding this teaser.

At present, the standard stock size of S-BAL42 is 145 mm wide. Adjusting to this size, and optimizing for the corresponding field, this 170 mm aperture lens results. Zonal figuring on the first surface of the inner lens can accurately reduce the nulls to very low levels.

With another glass (K3) for the last lens, the outer surfaces of the middle triplet become close enough to flat.

Here is a spectrum of doublet designs.

I found a relatively pleasing geometry for an 600 mm f/12 relay Cassegrain telescope. The base design here is a 600 mm f/10.8 Cassegrain, but with both mirrors left spherical, focussing about 70% of the way back toward the primary. A cemented doublet and a cemented triplet are placed into the divergent beam to refocus it just over 3/4 aperture behind the primary.     ATMOS     OSLO     TEXT     ZEMAX

A few years ago, Roland Christen provided a Petzval telescope design, consisting of two well-separated doublets. This particular design was aptly suited to ATM construction, in that the crown elements of each doublet are isoconvex and mated to the adjacent flint surfaces, simplifying both construction and testing. Discussions on the ATM Optics SW list led to an ECO design that uses an N-BK7/N-F2 air-spaced crown-first "primary" and a N-BK7/N-BAK4 cemented or oiled crown-first "secondary" (with N-BAK4 being the "flint") -- as in the Christen design, the glass selection here is intended to be robust, clean, and cheap-cheap-cheap (for optical glass, that is). Assuming a requirement for the best Visual Strehl (photopic), I parameterized this design over the f/7.5 to f/12.5 range, assuming a field diameter of 42 mm for a 200 mm aperture. In addition to being achromatic with correction of spherical aberration and coma, I required the design to be well-corrected for lateral color -- the principal rays of the C and F lines fairly well coincide at the field edge. Also, the tangential and sagitta image surfaces cross in a specific way within the field -- the residual longitudinal error is within 0.4 microns for 200 mm aperture designs.

Other nice features include relative compactness (for a Petzval -- the instrument lengths are only between 14.8 and 15.4 percent larger than the focal length ) and low field curvature (the radius of curvature is slightly larger than the focal length).

While the zonal correction would be improved by going to a more "flinty" last lens, doing so would run the risk of introducing stronger ghost reflections within the "primary".

As in the designs above, let F be the focal length, and v be the inverse of the f-number, f. As in the Christen design, the crowns are isoconvex and mated to the adjacent flint surfaces; the design only has four distinct curvatures:

     F*C2 = 1.889536316 - 1.336123523*v + 8.785302469*v² - 20.418954927*v³
     F*C5 = -0.012877806 - 1.769828845*v + 11.919432605*v² - 26.643048396*v³
     F*C6 = 4.061931292 - 3.128435549*v + 26.857730314*v² - 46.665807720*v³
     F*C8 = 2.325932130 - 0.646669024*v + 12.588103674*v² - 10.197740152*v³

The mean curvature of the green (e-line) image surface is also known:

     F*CI = -1.021771842 + 0.477072244*v - 2.094281811*v² + 6.660358951*v³

The semi-diameter of the "primary" is assumed to be 51 percent of the design clear aperture. To provide the same unvignetted field, however, the "secondary" semidiameter needs to increase as the f-number increases. The "secondary" semidiameter is assumed to be ( 26 + f / 18 ) percent of the design clear aperture. The lens thicknesses are derived from the semidiameters. The edge thickness of the "primary" and "secondary" crown elements is assumed to be 10.0 and 12.5 percent of the semidiameters, respectively. Similarly, the central thickness of the "primary" and "secondary" flint elements is assumed to be 12.5 and 14.0 percent of the semidiameters, respectively. The "primary" air-space is given by:

     T3/F = 0.004501449 - 0.047412957*v + 0.299151686*v² - 0.678818285*v³

while the "primary"-to-"secondary" separation is given by:

     T5/F = 0.794027739 + 0.017564617*v - 0.428311625*v² + 1.295904039*v³

The distance to the green (e-line) paraxial focus from the last lens surface is then:

     TG/F = 0.356603030 - 0.403530707*v + 1.700327564*v² - 5.326964118*v³

The location of the best Visual Strehl relative the the green paraxial focus depends on the aperture and f-number. I roughly determined these values as the sum of a variable offset and a fixed offset, using 100 and 200 mm clear apertures as gauges. The variable offset scales with clear aperture; the fixed offset remains the same. The table below provides these values, in mm, for the 200 mm clear aperture. Thus, for the 100 mm clear aperture, the variable offset will be half the given value, while the fixed offset will remain the same. Also provided are Visual Strehls for the 200 mm and 100 mm clear apertures.

I found a number of doublet designs that have good correction for spherical aberration. A table is given here.