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Home , Apochromat

THE MELIOR

A NePw ROefracCtingH TeleRscopOe OMptical ADesT ign

By Joseph Bietry

Refracting have de - veloped over centuries, from the humble beginnings of the Galilean to the modern apochromats of today. Advances in astronomical refractors often came about through improvements to optical materials that offered better control of color er - rors (). Occa - sionally, a different optical design offered improvements as well. This article will describe a new optical-de - sign form that offers improvements to chromatic aberration, as well as field of view beyond that of current refracting apochromatic telescopes. The name, the Melior Apochro - mat, was chosen for two reasons. First, the English translation for the Latin “melior” is “better” or “im - Figure 1: A simple with . proved,” and this is indeed a per - formance improvement over current apochromats. But of more impor - tance to me is that “Meliora” is the motto of my alma mater, the Univer - sity of Rochester. I was lucky enough to have studied lens design at the UR’s Institute of Optics under such greats as Rudolf Kingslake and Robert Hopkins. By using the root of the motto for the naming of this de - sign, I am honoring the University Figure 2: The upper half of a simple lens with spherical aberration. The plot at the right shows and the professors who gave me the the focus error with respect to the position of the ray within the aperture.

Astronomy TECHNOLOGY TODAY 69 THE MELIOR APOCHROMAT

parallel rays of light entering from the left of the lens represent an infinitely distant point of light (i.e. a star). Ideally, all of these rays should converge to a single point at the image plane, but because of spherical aberration, different radial zones of the lens focus at different locations along the optical axis. Figure 2 shows just the upper half of the lens. The optical axis and five rays are labeled with each ray representing a cer - tain radial distance away from the axis. Ray 1 is the ray nearest the optical axis and represents the position of the image Figure 3: A 3D model of the Melior Apochromat. plane (referred to as the paraxial focus). Ray 5 passes through the outer edge of the lens and strikes the axis inward from the paraxial image plane by a distance “z.” The plot to the right in Figure 2 shows this focus error with respect to the posi - tion of the ray within the aperture. The graph shows that the light pass - ing through this lens focuses more inward (towards the left) as the rays move closer to the edge of the lens aperture. This graphically represents spherical aberra - tion. The curve could be bending to the left (as illustrated) indicating under-cor - rected spherical aberration, or it could be Figure 4: A typical Petzval design – four elements arranged in two widely separated groups. bending to the right indicating over-cor - rection. In a perfect lens, all of the light knowledge and opportunity to pursue my bows are created. Spherochromatism would focus to a single point and all rays dreams. then, is simply the variation of spherical would cross the axis at the same location. The typical apochromat makes use of aberration with changes in . This would show in the graph as a modern optical materials to control chro - Anyone who has ground and polished a straight, vertical line. matic aberration. They are often referred Newtonian rec - Let us now turn our attention to the to as anomalous- glass or extra ognizes the importance of correcting details of the Melior Apochromat. The de - low-dispersion (or ED) glass. These ma - spherical aberration by figuring the sur - sign presented here has a 1000-mm focal terials are a significant improvement over face of the mirror to the shape of a length and a 155-mm (6.1-inch) entrance the common glass achromatic refractor parabola. Since a reflecting surface re - pupil diameter yielding an f/6.45 f-num - designs, but they still suffer from a resid - sponds the same to any color, once the fig - ber. ual color aberration known as sphe - uring is done, the spherical aberration is Figure 3 shows a 3D model of the rochromatism, and it is this error that removed for all of light. Such design. It has four elements separated into ultimately limits the performance of the is not the case for refracting surfaces. three sections. Starting from the left, the apochromat. Although it may sound To illustrate, I will describe a way to first section is a single common glass ele - complicated, the concept behind it is graph spherical aberration and then also ment, the second section is a with quite simple. When light refracts through graphically show how it changes with one anomalous glass element and one an optical material, it inherently responds wavelength (spherochromatism) for re - common glass element and the third sec - differently for different wavelengths (or fracting telescopes. Figure 1 shows a sim - tion is another single common glass ele - colors) of light in the same way that rain - ple lens with spherical aberration. The ment. Because of the very unusual

70 Astronomy TECHNOLOGY TODAY THE MELIOR APOCHROMAT distribution of glass types, this unique de - sign offers exceptional color correction and effectively eliminates spherochroma - tism. I have recently been awarded a patent that covers this new design concept (patent #9,588,331 issued on March 7, 2017). It would be instructive to compare the Melior Apochromat to other designs of similar caliber. Details of any optical design are always a closely guarded secret, so to make a comparison, I will need to design the comparison telescope using the same criteria that were used in the Melior design from known literature describing such design forms. The two most common apochro - Figure 5: A plot of the Melior Apochromat at various wavelengths from 400 nm (deep blue) to matic designs on the 700 nm (deep red). market today use either the Triplet or Pet - zval forms. The Triplet, as the name sug - gests, uses three refracting elements in close proximity to each other. The Petz - val, on the other hand, uses four elements in two widely separated groups. While minimizing the number of elements is one goal in a telescope design, a triplet type does not have the ability to operate at a focal ratio much faster than f/8 before per - formance begins to degrade. Since the Melior is operating at f/6.45 and is itself a four-element solution, a Petzval seems to be the most appropriate design against which to make comparisons. Figure 4 shows the resulting Petzval solution that I designed with the same cri - teria used to design the Melior. It is con - Figure 6: A plot at the same scale for the Petzval design at various wavelengths from 400 nm structed of two doublets that are widely to 700 nm.

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Astronomy TECHNOLOGY TODAY 71 THE MELIOR APOCHROMAT

of the colors in the Melior Apochromat have the same general shape and cluster together quite closely. The Petzval, on the other hand, clearly exhibits the issue of spherochromatism. At 400 nm, the graph curves strongly to the right indicating over-corrected spherical aberration. At 700 nm, the graph curves strongly to the left indicating under-correction. The range of focus error across all colors ex - ceeds 0.6 mm for the Petzval design, while the Melior contains all colors within a focus range of 0.15 mm; a four-times im - provement to that of the more conven - tionally color-corrected Petzval design. You may notice in the focus error plot of the Petzval design (Figure 6) that the Figure 7 colors tend to converge at between 0.7 to spaced. Each doublet is well corrected for nificant relief from spherochromatism. 0.8 (or 70 percent to 80 percent) in aper - color by using an anomalous glass (Ohara Figure 5 shows a plot as described ture height. For minimizing the impact of S-FPL53 in this case) element. The Petz - above for the Melior Apochromat at vari - spherochromatism, this is the desired lo - val-type design does an excellent job of ous wavelengths from 400 nm (deep blue) cation for the colors to converge. It is in - correcting primary and secondary color, to 700 nm (deep red), and Figure 6 structive to note that color correction in which allows it to be designated as an shows the same plot at the same scale for an optical design is usually reported at apochromat, but it does not offer any sig - the Petzval design. You will notice that all only this minimum aberration zone. ASTROONOMY FREE Subbscription OOffer! TECHNOLOOGY TODAY In celebrationa of our new diigital-centrici focus,o we are offere ingi thhreee special Your Complete Guide to Astronomical Equipment opportunities to sample our new format.o Therh e are no complicated coddes to remember!e astronomytechnologytoday.com Simply enter the word ““trial,i ” “club” or “education,” as approopriate.i

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72 Astronomy TECHNOLOGY TODAY THE MELIOR APOCHROMAT

Using that notion, it could be said that the Petzval design has approximately the same color correction as the Melior when looking at this zone only. However, when looking over the entire aperture of the tel - escope, the Melior has significantly supe - rior color correction and will focus more energy to the desired location. The graph in Figure 5 clearly shows a dramatic improvement in color correction for the Melior design, but it does not nec - essarily quantify how much better the tel - escope would perform in actual use. One way to convey that is to use a Strehl ratio. A Strehl ratio is a normalized metric to indicate how closely the optical system approaches theoretical perfection, and a Strehl ratio of 1.0 thus indicates a perfect Figure 8: Color sensitivity variation over wavelength for a dark-adapted eye. system. Typically, a Strehl ratio is only Petzval design (see Figure 6) is 450 nm, to the final image and should therefore be reported at a single wavelength (mono - since it is the color closest to a vertical line considered. I will use a particularly rigor - chromatic), and in the presence of sphe - in the graph. ous requirement and suggest that all wave - rochromatism, the wavelength is carefully The Melior, on the other hand, lengths will contribute equally to the chosen to be one that has very little spher - would have about the same Strehl ratio no system performance. This seems a reason - ical aberration. The wavelength that matter what color is chosen. In use, all able approach when using a camera, be - would offer the highest Strehl ratio for the wavelengths (polychromatic) contribute cause camera sensors have high sensitivity Howie Glatter’s Lasers The Blug™ Laser Collimators The innovative Blug™ - Our Collimators have long been recognized as short for Barlowed collima- the best in the industry. Available in several con- tion plug - is used with a figurations they are shockproof and hand ma- laser collimator to perform chined to < 0.00002” < 15 arc second beam perfect Barlowed laser alignment. Each laser is individually tested prior primary mirror alignment. to shipping and is complimented with various attachments and other parts. Priced at 1.25”- $35, 2”- $65 Priced at 1.25”- $75, 2”- $115 tuBlug™ Parallizer™ The tuBlug™ is the Blug™ for Keep it Square! Centering is nice, those who want to Barlow-colli- but parallelism is golden and the mate their primary from the back of Glatter Parallizer™ has a patented the scope, but have a solid tube Newtonian, or prefer not to have design that insures dead parallel to slide their shroud up. alignment between a 2” drawtube Priced at and a 1.25” accessory. 1.25”- $75, 2”- $115 Priced at Priced at $45

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Astronomy TECHNOLOGY TODAY 73 THE MELIOR APOCHROMAT

scope-optics.net/Strehl.htm). It can be seen that, as a result of spherochromatism, the Petzval design does not meet the dif - fraction limit with this uniform poly - chromatic criterion. The Melior calculates well above the minimum diffraction limit and is above 0.96 across the entire field of view. Both designs perform quite uni - formly across the plotted field of view of 1.55-degrees semi-field. For the given focal length of 1000 mm, this corresponds to an image-circle diameter of 54 mm. However, it should be noted that for both designs, I allowed the image surface to be curved. This minimizes the amount of astigmatism in the field, and it is my be - Figure 9 lief that defocus due to a curved field is a over a very large spectrum. 400 nm to 700 nm for a series of field an - more acceptable error than astigmatism. The plot in Figure 7 shows the poly - gles. It is conventionally accepted that a The Petzval design has an image ra - chromatic Strehl ratio with uniform Strehl ratio of 0.8 or better is considered dius of 817 mm and the Melior design has weighting over a wavelength range from diffraction limited (see http://www.tele - an image radius of 1041 mm. So, the Me -

74 Astronomy TECHNOLOGY TODAY THE MELIOR APOCHROMAT lior design naturally tends toward a flat - ter image surface than that of the Petzval design. These are both fairly long radii and for many uses may not cause any problems at all. For extremely demanding applications, there are well known tech - niques for adding a field flattener. While uniformly weighting the wave - lengths may be a reasonable approach for a camera system, it is overly pessimistic for visual uses. The human eye sensitivity varies significantly over the 400 nm to 700 nm range. When the eye is well dark adapted, it has a response to color known as scotopic vision (https:// en.wikipedia.org/wiki/Scotopic_vision). Figure 8 shows how this sensitivity varies over wavelength for a dark-adapted eye. The deep-red region has very little sensi - tivity, and the peak sensitivity is in in the blue-green region of 500 nm. The result of calculating the poly - chromatic Strehl ratio using the scotopic color weighting is shown in Figure 9 . The Melior Apochromat is little changed with this reduced spectrum weighting, indicat - ing that chromatic aberration is quite small over the entire wavelength range. The Petzval design using the scotopic weighting is improved to place it within the diffraction limited category (Strehl greater than 0.8) over most of the field, suggesting that chromatic aberration (specifically spherochromatism) is a sig - nificant contributor to polychromatic Strehl ratio. It can also be seen that there is some degradation at the edge of the field due to Figure 10: A Melior Apochramat prototype on a Celestron CGEM-DX mount. other aberrations. The Petzval appears to be reaching a limit in its field of view, sors of which I am aware. However, the Figure 10 is a photo of one of the whereas the Melior remains constant and Melior design could easily cover larger prototypes on a CGEM DX mount. To could easily be extended to larger fields of sensor formats, if desired. measure performance of the prototypes, I view without significant impact to image Yet, a theoretical design has no real am using a double-pass (also known as quality. Both designs were only optimized value if it can’t be built. The worth of a auto-collimation) static fringe interfer - over the 1.55-degree semi-field of view, design is only realized if it delivers high ometer. Figure 11 is a photo of a double- but when analyzed at 2.0-degrees semi- quality when constructed. To satisfy my - pass interference pattern using a Helium field, the Melior performance is un - self that this is indeed a design that can be Neon red laser (632.8 nm) at a field angle changed at 0.96 Strehl, while the Petzval built, I set off to build a few prototypes. of 0.5 degrees. drops to 0.64 Strehl. I chose the 1.55-de - Four prototypes have been built to date, I used the program called FringeXP gree field to cover the largest camera sen - and all have performed admirably. to analyze the captured fringe patterns,

Astronomy TECHNOLOGY TODAY 75 THE MELIOR APOCHROMAT

and a Strehl ratio was calculated from that image. I captured interferograms at red Helium Neon (632.8 nm) and green He - lium Neon (543.5 nm). The plot of Strehl ratio versus angular semi-field of view for one of the built prototypes is shown in Figure 12 . All of the prototypes have ex - hibited nearly identical measured per - formance suggesting a build consistency even with variations from part to part. The prototypes now are in the skilled hands of a few expert amateur as - tronomers. They will make evaluations of the telescope – both visually and photo - graphically – to see how this design im - provement translates into better observing. Assuming the field testing is positive, where do we go from here? If there is in - terest from the astronomy community, I would like to consider making a produc - tion run of telescopes. I chose a 6.1-inch aperture for the prototype, because it ap - peared to be a popular diameter for re - fractors, and this could be the first product. However, I think the real value in this design is in larger apertures. Since the spherochromatism of the Melior is unusually well controlled, scaling the de - Figure 11: Photo of a double-pass interference pattern of a Melior Apochromat prototype sign up to a larger aperture does very lit - using a Helium Neon red laser (632.8 nm) at a field angle of 0.5 degrees. tle to diminish performance. I have an 8.1-inch (205-mm) diameter 1325-mm focal length (f/6.46) design on the draw - ing board right now that has very nearly the same level of performance as its smaller counterpart. I present a new refracting telescope optical design in this article. It exhibits ex - ceptional performance both theoretically as well as in telescopes that have been con - structed. I compare it to other types of apochromatic telescopes to show how this improved design translates into actual per - formance metrics. It is not my intention to disparage the quality of the other de - signs. The Petzval and triplet apochromats are quite excellent telescopes. But for very demanding applications, particularly with larger apertures, the Melior Apochromat Figure 12 offers a unique advantage.

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