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Abstract
Maresse described a classical solid catadioptric system (SoCatS) for a lens comprising a solid body and a single-focal Maksutov type construction, characterized by two refractive and two reflective surfaces. Due to ray propagation through the solid block twice, the design is feasible at a single wavelength, otherwise suffering on chromatic aberration induced by dispersion. We design a SoCatS for a telescope and describe a class of solutions to reduce and control chromatic and some spherical aberration in the solid catadioptric system.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Compact solid telescope (SoCatS)
A Ritchey-Chretien (R-C) telescope, as for example the Hubble space telescope, is a two-mirror on-axis all reflecting optical system, with a central obscuration. Each mirror has a different set of high order a-spherical coefficients to correct aberrations, including spherical, coma and astigmatism. We previously designed an R-C telescope in the visible (VIS) for surveying the Martian surface to select the area that might be suitable for landing the rover and for its initial exploration [1]. Thinking about additional uses of the telescope as a surveillance camera to search for infrared (IR) signature of the geological contents and minerals on the Martian surface, we incorporated several lenses to permit imaging also in the IR [2]. The instrument design thus included reflecting and refracting components, making it a catadioptric system. A solid catadioptric system (see Fig. 1) simply squeezes, or brings closer together, two mirrors in the R-C telescope, filling with glass the air-gap between them [3–10].
Fig. 1 Ray trace in the SoCatS with a monolithic body. The stop is located at the secondary mirror for better aberration control.
2. Design method for IR and visible
The all-mirror R-C design is free of chromatic aberration, being an assembly of mirrors [11]. When a suitable solid, transparent medium, called glass for simplicity, fills the space between the two mirrors, each surface, perpendicular to the optical axis in the paraxial approximation, that encloses the solid glass is both reflective and transmissive. These features are incorporated in different radial positions measured from the optical axis. If we follow the trajectory of a typical ray in Fig. 1, we see that the first surface that is encountered is transmissive only in the annular region outside the secondary mirror that actually acts to the incoming rays as an obstruction, just as in the traditional reflective telescopes. The rays may be refracted at the outer annular region of the first surface encountered, depending on their angle of incidence. From there they travel onto the second surface enclosing the solid block. They reflect at the outer annulus of this surface that functions as the primary mirror. From there they reflect and are incident onto the secondary mirror occupying the inner circle of the first surface of the solid block. Both outer annulus of the primary mirror and inner circle of the secondary mirror are coated with a reflective coating on the outside. Both outer annulus of the first surface and the inner circle of the second surface may be coated with an antireflection coating to decrease stray light noise and increase throughput. From the secondary mirror the rays reflect through the second transparent surface of the solid block and onto the detecting EO assembly.
This system has been called the Solid Catadioptic System, or SoCatS, in short. We note that the letter “r” is missing in comparison with the similar earlier designation. In the traditional SoCatS, this block is fabricated from a single optical material that we have been referring to as “glass”. Therefore, it suffers from an appreciable amount of chromatic aberration when used over an extended spectral interval, requiring additional corrective components. Usage over a spectral band results in the image quality degradation and performance deterioration, especially in the visible, due to its relatively short wavelength as compared to those in IR, and relatively wide spectral interval. Wavelength width over average wavelength for visible is about 1, while it is 0.4 for the long-wavelength IR atmospheric window. Therefore, the performance deterioration over a wide spectral region is a lesser issue in the IR. Nevertheless, it cannot be neglected there either, at least not for the high-resolution applications.
Conceptual tunnel diagram analysis includes the following ray trajectories. Essentially, the R-C telescope is composed of a pair of positive and negative mirrors. In Fig. 1, featuring a SoCatS design for the IR, we see that the optical function from Surface 1 to Mirror 1 is equivalent to a positive lens; from Mirror 1 to Mirror 2, the optical power is equivalent to another (different) positive lens; and from Mirror 2 to the exit Surface, the function is equivalent to that of a negative lens. In our model we consider the two positive lenses as a positive doublet lens. The positive doublet and the negative lens in SoCatS are similar to the positive and negative mirror in the traditional R-C design. The doublet consisting of equivalent positive and negative lens is modeled in the paraxial system for control of the chromatic aberration. Thus, a monolith block of Fig. 1 is also modeled as a doublet.
3. Control of chromatic aberration in a cemented doublet
The classical paraxial treatise on chromatic aberration can be found in most optical design textbooks [12–14]. We model the chromatic aberration color correction as in a two-lens system, a cemented doublet. The governing equations for controlling axial color are:
Here, Φ1, Φ2, and Φ are the optical powers for element 1, 2, and the doublet; we denote with ν1, ν2 the Abbe numbers for the element 1 and 2, respectively; and f is the system (doublet) focal length. Considering that ν is a quantity that is always positive for optical glasses, we are searching for a combination of a positive and negative lens in the doublet. We expect that there will be many of those sets available to a designer to meet his specific design objectives. The following expressions may be solved from Eqs. (1) and (2). The powers have opposite signs, for a positive and negative lens. The absolute value of the optical power of each lens is proportional to its Abbe number, and inversely proportional to the system focal length and the difference in their Abbe numbers. A significant reduction in the chromatic aberration may be achieved in the design by incorporating optical elements fabricated from materials, displaying large differences in their Abbe numbers.4. SoCatS as a monolith block for IR applications
For IR the new SoCatS design concept methodology recommends the employment of a single substrate. Figure 1 features the SoCatS for the applications in the IR. On the basis of Eqs. (3) and (4), we seek material with low index of refraction n and high ν as the rule for selecting materials for the device used in the IR to achieve the full potential of the new instrument.
Some example materials would include germanium (Ge), gallium arsenide (GaAs), and silicon (Si) (Group 1), all popular materials for the IR optical systems. They feature a high index of refraction for reducing spherical aberration, accompanied with high ν. However, higher index of refraction of the material in SoCatS, as a single block, prohibits its optimal performance. The materials in the second group (Group 2), zinc selenite (ZnSe), zinc sulfite (ZnS), Amtir1 (IRG100) have similarly high Abbe number ν with lower value for the index of refraction n than materials in Group 1. These materials will provide a correspondingly better image quality, with respect to the correction of the chromatic aberration.
A popular material calcium fluoride (CaF2) exhibits a much lower index of refraction n than the above two groups. However, due to its lower Abbe number ν, it cannot deliver a diffraction-limited performance. Potassium bromide (KBr), featuring a higher Abbe number ν and slightly higher index of refraction n than that of calcium fluoride (CaF2), provides a nearly diffraction-limited image quality. We chose it for the design presented in Fig. 1.
The exit surface in IR applications may be a-spherized to meet stringent high performance requirements and to achieve the diffraction limit. Radiation resistant glasses are mandatory for the space application. There are 7 glasses (crown and flint) available from the Schott catalogue, for example.
We present the modulation transfer function (MTF) of the monolith telescope, designed for 4.2 by 4.2 degrees FOV in Fig. 2 for spectral interval 8 to 12 μm (Fig. 2) and in Fig. 3 for the one 3 to 5 μm (Fig. 3). The MTFs are displayed for several field positions in degrees. Figures 4 and 5 exhibit the spot diagrams of the monolith telescopes, designed for 4.2 by 4.2 degrees field-of-view (FOV) and F/# of 4.3. We show the performance for the IR spectral intervals, from 8 to 12 μm in Fig. 4) and from 3 to 5 μm in Fig. 5. The spot diagrams in Figs. 4, 5, and 8 are presented for several field positions: Figure element (1,1) is on axis; Figs. (1,2), (1,3) and (1,4) are for field angles (0.5, −0.5) deg., (1.0,1.0) deg. and 1.5, 1.5) deg. Rows 2 and 3 are for field angles (1.7,1.7) deg. and (2.1,2.1) deg. for all four quadrants. Figures 4, 5, and 8 are scaled, so the spot sizes are approximately the same.
Fig. 2 Polychromatic MTFs of the monolithic SoCatS as a function of spatial frequency, for spectral interval 8.0 to 12.0 μm and FOV of 4.2 by 4.2 degrees. The MTFs are shown for several field positions in degrees and compared with the diffraction limited MTF.
Fig. 3 Polychromatic MTFs of the monolithic SoCatS as a function of spatial frequency, for spectral interval 3.0 to 5.0 μm and FOV of 4.2 by 4.2 degrees. The MTFs are shown for several field positions in degrees and compared with the diffraction limited MTF.
Fig. 4 Polychromatic spot diagrams of the monolithic SoCatS for spectral interval 8.0 to 12.0 μm and FOV of 4.2 by 4.2 degrees. The spot diagrams are presented for several field positions.
Fig. 5 Polychromatic spot diagrams of the monolithic SoCatS for spectral interval 3.0 to 5.0 μm and FOV of 4.2 by 4.2 degrees. The spot diagrams are presented for several field positions.
Table 1 lists the parameters of interest: average wavelength, diffraction limited spot size, root mean square spot size, and geometrical spot size for visible, midIR and farIR spectral bands. System requirements are FOV = 4.2 by 4.2 degrees, F/# = 4.3.
Table 1. Spot size parameters for Figs. 4, 5 and 8. System requirements are FOV = 4.2 by 4.2°, F/# = 4.3.
5. SoCatS with cemented doublet for decreased chromatic aberration in the visible, 0.4 μm to 1 μm
For the visible applications, the new SoCatS design concept recommends splitting the solid block into two pieces with different substrate materials and then cementing them together. This idea is illustrated in Fig. 6, featuring the SoCatS for applications in the visible.
Fig. 6 A cemented SoCatS doublet featuring two different substrates for applications requiring additional control of chromatic aberration, as in the visible 0.4 μm – 1 μm. The stop at the secondary mirror provides better aberration control.
Similarly to the traditional R-C, the high order a-spherical coefficients of the two mirrors are used to enhance or compensate and control spherical, coma and some astigmatism, all with the objective of achieving diffraction limited performance.
Figure 7 presents the MTF of the cemented doublet telescope, designed for 4.2 by 4.2 degrees FOV. We show the performance in the visible range, from 0.4 to 1.0 μm, for several field angles. Figure 8 displays the spot diagram of the cemented doublet telescope, designed for 4.2 by 4.2 degrees FOV and 0.4 to 1 μm. The spot diagrams are displayed for several field positions. Table 1 lists the parameters of interest.
Fig. 7 Polychromatic MTFs of the cemented SoCatS as a function of spatial frequency, from 0.4 to 1.0 μm and FOV of 4.2 by 4.2 degrees. The tangential MTFs are shown for several field positions in degrees and compared with the diffraction limited MTF.
Fig. 8 Polychromatic spot diagrams of the monolithic SoCatS for spectral interval 0.4 to 1.0 μm and FOV of 4.2 by 4.2 degrees. The spot diagrams are presented for several field positions.
For commercial and non-space applications, optical materials suitable for precision molding may be used. The two thick, lenses formed from different materials, may be molded separately and then cemented together at a later time, possibly after the application of coatings on outer surfaces. There exist 27 glasses (crown and flint) suitable for molding, available from the Schott catalogue.
The exit surface may also be a-sphericized for meeting additional high-performance requirements to achieve a close to, or even better than, diffraction-limited image quality. Such improvements would potentially imply additional cost for mold making or for diamond-machining the outer surface.
6. Summary
We presented a novel design methodology to achieve (nearly) diffraction-limited performance of a solid, short SoCatS telescope, suitable for use from 0.4 to 15 μm, based on optical design principles of achromatic doublet in the visible. The novel design method has two significant features: it is compact and short; and it nearly completely reduces and/ or removes chromatic and spherical aberrations as compared to all prior solid catadioptic systems. Two appropriately selected, different materials are employed in the visible, while a single material is incorporated for the IR.
We described three design examples to illustrate the novel design methodology, two that are suitable for traditional IR applications, incorporating a monolith block, and a third one for the visible to near IR applications employing a cemented doublet. This optical design methodology, and its model, is an excellent building block for more complex optical systems, including surveillance cameras, objectives, zoom lenses, and professional movie cameras.
The device implementation concepts and method exhibit many benefits over existing systems. The SoCatS is compact, having the ratio of the total optical path length to the effective focal length of about 0.6 or less. This is smaller than the telephoto ratio in commercial telephoto lenses. Its compact size and lightweight make it highly advantageous for commercial, space, and military applications.
The novel idea of the cemented doublet in the visible greatly improves the image quality for commercial, ground observatory, NASA and DOD remote sensing and surveillance applications. The possibility of using the molding process makes this system particularly attractive for commercial applications or in telescope arrays.
The central obscuration due to the secondary mirror and the compactness in the optical train greatly restrict the field of view (FOV) to less than 5 by 5 degrees and the focal ratio remains larger than F/4. The possibilities for further improvements exist due to some residual spherical and 2nd order axial color, leading to development and interesting future research in optical design.
Acknowledgments
The authors wish to express their appreciation to B. Bravo-Medina and M. K. Scholl for helpful discussions. This material is based upon work partially supported by the Air Force Office of Scientific Research under award number FA9550-18-1-0454. Any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force.
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