Two Designs for the USNO dFTS Back-End Lens Assembly

Astronomical Applications Dept.

U.S. Naval Observatory, Washington, DC

murison@usno.navy.mil

13 March, 2007

Abstract The USNO dispersed fourier transform spectrometer (dFTS) "camera" resides at the back end of the dFTS, downstream of the dispersing element (a transmission diffraction grating). It consists of a commercial CCD camera ( $2048 \times 126$ 12-micron square pixels) with a custom lens assembly sitting between the diffraction grating and the CCD. The purpose of the lens assembly is to capture the dispersed fringes leaving the grating, within the nominal bandpass, and focus them onto the CCD, preferably packing the point spread function into a single pixel. The optical design upstream of the dFTS puts a 60 mm diameter beam on the grating and requires an effective focal length of 85 mm for the back-end lens assembly and hence a roughly f/1.2 design. The current bandpass is 450-600 nm. Thus, the field angle of the lens assembly must accomodate a 16.6 $°$ span in the dispersion direction while the light must be focused onto a 12 micron or smaller spot across the bandpass. Many lens designs were developed, optimized, and analyzed, resulting in the two lens designs presented here. To varying degrees, they meet (or nearly meet) all of the requirements. In particular, a seven-element design incorporating one radially aspherical surface well exceeds the requirements while, according to tolerance analyses, still appearing to be manufacturable at reasonable cost. After considerable effort, it was determined that inexpensive catalog lenses cannot be made to fit the requirements. Hence, four or five custom lenses (in addition to three catalog lenses) are necessary. The designs are optimized with an eye toward gentle (and hence inexpensive) surface curvatures. Fortunately, all surfaces — aside from the single asphere in the best design — are spherical and hence easy to grind and polish. The lens assemblies are six to seven inches in total track (grating to CCD). With high-quality coatings, throughput should be 92-93 percent.

Subject headings: optics—optical design—lens—fourier transform spectrometer

The XML version of this document is available on the web at
http://murison.alpheratz.net/papers/FTS/FTS_Camera_Lens_Designs.xml

The PDF version of this document is available on the web at
http://murison.alpheratz.net/papers/FTS/FTS_Camera_Lens_Designs.pdf

1 Introduction

1.1 The dFTS Context

1.2 Performance Requirements of the Back-End Lens Assembly

2 Final Designs of the Back-End Lens Assembly

2.1 Best: An Asphere Design

2.2 Backup: An All-Spherical Design

3 References

4 Appendix A: Glass Properies

5 Appendix B: Zemax Prescription for the Radial Asphere Design

6 Appendix C: Zemax Prescription for the All-Spherical Design

1 Introduction

1.1 The dFTS Context

Figure 1 is a block diagram showing the major dFTS components. Starlight from a telescope is focused into the cone of acceptance of an optical fiber which then transmits the light to the front end of the dFTS. After conversion to interferometric fringes in the FTS, the light is focused onto a lenslet array, sent through a set of fibers to a collimator, and then on to a diffraction grating, where dispersion occurs. Following the grating, a camera lens assembly focuses the light onto a CCD detector. There are two configurations of the back-end lens assembly in order to accomodate each of two anticipated telescopes to which the dFTS may be attached. The first, and simpler, version has the effective focal length 300 mm, while for the second version the effective focal length is much shorter at 85 mm. For both versions, all else is the same, at least for our purposes here. Since the 85 mm version has the most stringent requirements, that is the one analyzed and presented here. Similar design considerations and analyses were applied to the 300 mm version.

$FTS block diagram$

Figure 1: Block diagram of the dFTS system. Version 1 (85 mm EFL) of the back-end assembly is shown in black, and version 2 (300 mm EFL) is in red.

1.2 Performance Requirements of the Back-End Lens Assembly

We have several constraints on the design of the back-end lens assembly. Because of other system constraints occuring upstream in the light path, the effective focal length (EFL), $f$ , of the back-end lens assembly must be near 85 mm. Additionally, the detector in the dispersion direction spans $d = 2048 \times 12 μ m = 24.58 mm$ . Thus, the field angle $θ$ that the lens system must be able to accomodate is

\tan \frac{θ}{2} \geq \frac{d}{2 f}

(1)

or $θ ≳ 16.6 °$ . The field lens of the assembly will be no closer than a distance $s$ of approximately one inch from the 60 mm pupil located on the diffraction grating. Hence, letting $b$ denote the beam diameter at the grating (i.e., the image pupil diameter), the physical diameter $D$ of the field lens must be at least

\frac{D}{2} \geq \frac{b}{2} + s \tan \frac{θ}{2} = \frac{b}{2} + \frac{d}{2 f} s

(2)

or $D ≳ 68 mm$ , to avoid vignetting in the dispersion direction at the entrance aperture. Unfortunately, most readily-available catalog lenses have diameters of 50 mm or less.

Further major requirements are as follows:

The optical system must accomodate a bandpass of 450 nm to 600 nm. In this bandpass, stellar absorption line density is maximal for the lower main sequence stars to be observed by the dFTS.
The system throughput, which is an overriding concern, must be maximized by capturing as much as possible of the PSF into one pixel (a $12 μ m$ square).
The air-glass interfaces must transmit as much of the incident light as possible. This will require good-quality antireflection coatings, which, fortunately, are now readily available. Transmissions of 99.5 percent or greater are possible at reasonable cost across our bandpass. An eight-lens system (16 exposed surfaces) would then have an ideal transmission of roughly ${0.995}^{16} \approx 0.92$ , or about 92 percent. This is significantly better than the approximately 10 percent (measured) transmission we are currently getting from the 85 mm f/1.2 Canon lens currently being used.
Due to instrument housing size contraints, the entire back-end lens assembly must fit within a total track of about a foot or less.

2 Final Designs of the Back-End Lens Assembly

2.1 Best: An Asphere Design

Cost considerations dictated that the designs would need to be built up starting with the simplest possible configuration. Thus, two achromats were located, after an exhaustive search of the standard optics catalogs, which together yielded an approximately 85 mm effective focal length. The first achromat, from Rolyn, has an effective focal length $f_{1} = 200 mm$ , while the second, from Melles-Griot, has $f_{2} = 125 mm$ . From thin lens theory, one can show that the effective focal length of the combination is approximately

\frac{1}{f} \approx \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}}

(3)

where $d$ is the distance between the respective principal planes (roughly, the distance between the centers of the achromats). Thus, a distance $d \approx 31 mm$ yields $f = 85 mm$ . The achromats are by definition partially corrected on-axis for chromatic aberration, so the on-axis focus over our bandpass is decent. But off-axis ray aberrations are many and severe, so a system consisting of just a pair of achromats is inadequate without further and substantial correction.

After consultation with books (e.g.[1], [2], [3], [5]) and lens system designs for other instrument cameras (mostly NASA-funded, available on the web), and after a great deal of experimentation — which will not be recounted here — an intuition was developed regarding the kinds of surfaces and corrections needed to achieve our requirements. (The human brain is amazingly adept at pattern recognition.) After many subsequent design variations and optimizations, a seven-element design eventually emerged as our top contender for fabrication. (The catalog achromats count as one element each.)

A brief summary of the process is as follows. Starting with the achromats, no requirements other than effective focal length are met at that point. From this crude begining, further lenses were successively added in such a way as to move the transverse size of the PSF simultaneously in the blue, green, and red towards the 12 micron requirement. This was greatly complicated by the large field angle and the fairly wide bandpass. Eventually, it was found that a system of eight lenses approximately met all the criteria. When the surface of one of them was allowed to take the shape of a radial asphere (the sagitta is a polynomial function of radius), performance increased dramatically and one of the other lenses, after compensatory re-optimizations, could be removed, resulting in a seven-element system. After the many iterations of optimization of lens parameters was completed, it turned out that, with subsequent re-optimization, the field flattening lens (see Fig. 2) could be replaced by a catalog lens. This worsened performance, but there was enough margin to still meet requirements. The glass properties were optimized for some of the custom lenses, then set to nearly-matching standard glass types (with subsequent re-optimization of the other parameters).

Table 1 summarizes the geometric optics spot diameters. The RMS spot diameters, which are a better indicator of performance than the geometric diameters, are all well inside the 12 micron requirement. Figures 2 and 3 show the layout of the final asphere design. Lens and positioning details are given in the Zemax (see [8]) prescription shown in Appendix B (Section 5). The glass types used in the two designs and their dispersions and refractive indices are summarized in Appendix A (Section 4). The total track is well within requirements.

Figure 4 shows the point spread functions at the bandpass end- and mid-points. Performance is nearly diffraction limited at the center of the bandpass. Performance at the blue end is slightly better at the blue end than at the red end. Even at the red end, all of the light fits within a $12 \times 12$ micron CCD pixel.

Table 1: RMS and geometric (i.e., total) spot diameters at the ends and center of the bandpass for the 7-element asphere design. Total track is the on-axis geometric path from grating surface to CCD.
spot diameters (microns):
	450 nm	525 nm	600 nm
RMS	4.0	4.4	4.2
geometric	13.8	9.2	18.0
EFL = 85.0 mm
total track = 181.5 mm

$85mm asphere layout 2D$

Figure 2: 2-D layout of the 7-element asphere design. Lens 7 (numbered left to right) serves as a field flattener and must lie as close to the CCD as practicable. Very slight vignetting occurs at lens 3. Catalog lenses are lenses 2, 5, and 7.

$85mm asphere layout 3D$

Figure 3: 3-D layout of the 7-element asphere design.

$85mm asphere PSF RGBsummary$

Figure 4: PSFs at the end and center wavelengths of the bandpass for the 7-element asphere design.

2.2 Backup: An All-Spherical Design

We are unsure of the added expense due to the special-order radial asphere in the previous design. Thus, as a back up, another design was built from the ground up using only lenses with spherical surfaces. The following eight-element design resulted.

Starting again with just the achromats, lenses were successively added and glass types optimized then matched to available glass, similarly to the previous design. Again, it was found that a system of eight lenses could approximately meet all the requirements.

Table 2 shows the geometric optics spot diameters. The RMS spot diameters are pushing against the 12 micron requirement in the green and blue. Figures 5 and 6 show the optical element layout. Lens and positioning details are given in the partial Zemax prescription of Appendix C (Section 6). Again, the total track is well within required bounds.

Figure 7 shows the point spread functions at the bandpass end- and mid-points. Performance is substantially poorer than with the asphere design, but still acceptable. The blue end of this design clearly suffers the most. Even so, nearly all of the light again falls within the confines of a $12 \times 12$ micron CCD pixel.

Table 2: RMS and geometric (i.e., total) spot diameters at the ends and center of the bandpass for the 8-element all-spherical design. Total track is the on-axis geometric path from grating surface to CCD.
spot diameters (microns):
	450 nm	525 nm	600 nm
RMS	12.8	11.6	7.6
geometric	50.4	20.0	21.2
EFL = 85.0 mm
total track = 175.7 mm

$85mm spheres layout 2D$

Figure 5: 2-D layout of the 8-element all-spherical design. Lens 7 (numbered left to right) serves as a field flattener and must lie as close to the CCD as practicable. Catalog lenses are lenses 2, 5, and 8.

$85mm spheres layout 3D$

Figure 6: 3-D layout of the 8-element all-spherical design.

$85mm spheres PSF RGBsummary$

Figure 7: PSFs at the end and center wavelengths of the bandpass for the 8-element all-spherical design.

3 References

[1] Born, M., and Wolf, E. (1999). Principles of Optics, 7th ed., Cambridge University Press, Cambridge, UK.

[2] Hecht, E., and Zajac, A. (2002). Optics, 4th ed., Addison-Wesley, Reading, Massachusetts.

[3] Rutten, Harrie G. J., and Van Venrooij, Martin A. M. (1988). Telescope Optics : Complete Manual for Amateur Astronomers, Willmann-Bell, Richmond, Virginia.

[4] Schott North America, http://www.us.schott.com/optics_devices/english/

[5] Suiter, Harold R. (1994). Star Testing Astronomical Telescopes: A Manual for Optical Evaluation and Adjustment, Willmann-Bell, Richmond, Virginia.

[6] Wikipedia (2006), "Abbe Number", http://en.wikipedia.org/wiki/Abbe_number

[7] Wikipedia (2006), "Glass Code", http://en.wikipedia.org/wiki/Glass_code

[8] ZEMAX Development Corporation, 3001 112th Avenue NE, Suite 202, Bellevue, WA 98004-8017, http://www.zemax.com/zemax/

4 Appendix A: Glass Properies

Table 3: Glasses used in the two designs, where "glass" is the Schott glass catalog designation (see [4]), and "glass #" is the international glass code (see, e.g., [7]). Cost is a rough estimate relative to BK7. Density is $g {cm}^{- 3}$ . Indices of refraction are at wavelengths in nm corresponding to the Fraunhoffer C, d, and F lines: $[(656.27, H), (587.56, He), (486.13, H)]$
glass	glass #	type	cost	$ρ$	$n_{C}$	$n_{d}$	$n_{F}$	$V_{d}$
LF50	589514	crown	1.7	3.11	1.58549	1.58893	1.59695	51.37
BK7	517642	crown	1.0	2.51	1.51432	1.51680	1.52238	64.17
SF5	673322	flint	1.5	1.98	1.66661	1.67270	1.68750	32.21
N-LAK33	754524	crown	11.5	4.26		1.75398		52.43
SF8	689312	flint	2.3	4.22	1.68250	1.68893	1.70460	31.18
N-SSK8	618498	flint	2.4	3.27	1.61400	1.61773	1.62641	49.8
SF11	785258	flint	3.0	4.74	1.77599	1.78472	1.80645	25.76
N-BAK2	540597	crown	1.4	2.86	1.53721	1.53996	1.54625	59.7
B270	523586	crown				1.523		58.6

$Abbe-diagram$

Figure 8: Abbe number (dispersion) and index of refraction for various glass families. (credit: [6])

5 Appendix B: Zemax Prescription for the Radial Asphere Design

A partial listing of the Zemax[8] prescription for the seven-element design incorporating a radial even asphere on one surface is as follows.

System/Prescription Data

File : D:\FTS\optics\back end 2006\back end -- catalog lenses 13m1.zmx

Title: Lens has no title.

Date : TUE MAR 13 2007

GENERAL LENS DATA:

Surfaces : 18

Stop : 1

System Aperture : Entrance Pupil Diameter = 60

Glass Catalogs : Schott OLD_SCHO HIKARI SCHOTT_2000

Ray Aiming : Off

Apodization :Uniform, factor = 0.00000E+000

Effective Focal Length : 85.01204 (in air at system temperature and pressure)

Effective Focal Length : 85.01204 (in image space)

Back Focal Length : 1.079896

Total Track : 181.4918

Image Space F/# : 1.416867

Paraxial Working F/# : 1.416867

Working F/# : 1.415121

Image Space NA : 0.3327782

Object Space NA : 3e-009

Stop Radius : 30

Paraxial Image Height : 12.41707

Paraxial Magnification : 0

Entrance Pupil Diameter : 60

Entrance Pupil Position : 0

Exit Pupil Diameter : 51.0616

Exit Pupil Position : -72.26761

Field Type : Angle in degrees

Maximum Field : 8.31

Primary Wave : 0.45

Lens Units : Millimeters

Angular Magnification : 1.175051

Fields : 3

Field Type: Angle in degrees

# X-Value Y-Value Weight

1 -8.310000 0.000000 1.000000

2 0.000000 0.000000 1.000000

3 8.310000 0.000000 1.000000

Vignetting Factors

# VDX VDY VCX VCY VAN

1 0.000000 0.000000 0.000000 0.000000 0.000000

2 0.000000 0.000000 0.000000 0.000000 0.000000

3 0.000000 0.000000 0.000000 0.000000 0.000000

Wavelengths : 3

Units: Microns

# Value Weight

1 0.450000 1.000000

2 0.525000 1.000000

3 0.600000 1.000000

SURFACE DATA SUMMARY:

Surf Type Comment Radius Thickness Glass Diameter Conic

OBJ STANDARD Infinity Infinity 0 0

STO STANDARD IMAGE PLANE Infinity 25 60 0

2 EVENASPH CUSTOM 1: ASPHERE -100 7 BALF50 75 0

3 STANDARD Infinity 1 75 0

4 STANDARD ROLYN 200 22.0306 122.6994 17 BK7 75 0

5 STANDARD -93.19664 3 SF5 75 0

6 STANDARD -267.7376 1 75 0

7 STANDARD CUSTOM 2 85 12.6748 N-LAK33 75 0

8 STANDARD -736.3267 26.84713 75 0

9 STANDARD CUSTOM 3 -137.0047 16.48535 SF8 60 0

10 STANDARD 139.5663 8.082863 60 0

11 STANDARD M-G 125 LAO817 80.927 27 N-SSK8 75 0

12 STANDARD -70.712 7 SF11 75 0

13 STANDARD -275.657 1 75 0

14 STANDARD CUSTOM 4 42.97554 18.10171 N-BAK2 40 0

15 STANDARD 61.52988 7 40 0

16 STANDARD ROLYN -76 12.0045 -39.85493 2.3 B270 30 0

17 STANDARD Infinity 1 30 0

IMA STANDARD Infinity 24.80518 0

SURFACE DATA DETAIL:

Surface OBJ : STANDARD

Surface STO : STANDARD IMAGE PLANE

Surface 2 : EVENASPH CUSTOM 1: ASPHERE

Coeff on r 2 : 0.0022451424

Coeff on r 4 : -4.1408001e-009

Coeff on r 6 : -1.3574831e-011

Coeff on r 8 : 0

Coeff on r 10 : 0

Coeff on r 12 : 0

Coeff on r 14 : 0

Coeff on r 16 : 0

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 3 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 4 : STANDARD ROLYN 200 22.0306

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 5 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 6 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 7 : STANDARD CUSTOM 2

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 8 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 9 : STANDARD CUSTOM 3

Aperture : Floating Aperture

Maximum Radius : 30

Surface 10 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 30

Surface 11 : STANDARD M-G 125 LAO817

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 12 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 13 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 14 : STANDARD CUSTOM 4

Aperture : Floating Aperture

Maximum Radius : 20

Surface 15 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 20

Surface 16 : STANDARD ROLYN -76 12.0045

Aperture : Floating Aperture

Maximum Radius : 15

Surface 17 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 15

Surface IMA : STANDARD

EDGE THICKNESS DATA:

Surf X-Edge Y-Edge

STO 20.813774 20.813774

2 11.186226 11.186226

3 6.870925 6.870925

4 3.251623 3.251623

5 8.238273 8.238273

6 12.358448 12.358448

7 3.000000 3.000000

8 24.477758 24.477758

9 23.072656 23.072656

10 14.033238 14.033238

11 7.024673 7.024673

12 15.199911 15.199911

13 8.500076 8.500076

14 16.505437 16.505437

15 0.728357 0.728357

16 5.230474 5.230474

17 1.000000 1.000000

IMA 0.000000 0.000000

INDEX OF REFRACTION DATA:

Surf Glass Temp Pres 0.450000 0.525000 0.600000

0 20.00 1.00 1.00000000 1.00000000 1.00000000

1 20.00 1.00 1.00000000 1.00000000 1.00000000

2 BALF50 20.00 1.00 1.60128826 1.59330461 1.58822114

3 20.00 1.00 1.00000000 1.00000000 1.00000000

4 BK7 20.00 1.00 1.52531950 1.51986781 1.51629483

5 SF5 20.00 1.00 1.69585207 1.68066679 1.67142879

6 20.00 1.00 1.00000000 1.00000000 1.00000000

7 N-LAK33 20.00 1.00 1.76936319 1.75946138 1.75308191

8 20.00 1.00 1.00000000 1.00000000 1.00000000

9 SF8 20.00 1.00 1.71347577 1.69736368 1.68759081

10 20.00 1.00 1.00000000 1.00000000 1.00000000

11 N-SSK8 20.00 1.00 1.63113017 1.62245679 1.61696192

12 SF11 20.00 1.00 1.81905382 1.79633638 1.78288949

13 20.00 1.00 1.00000000 1.00000000 1.00000000

14 N-BAK2 20.00 1.00 1.54960763 1.54340900 1.53939614

15 20.00 1.00 1.00000000 1.00000000 1.00000000

16 B270 20.00 1.00 1.53261969 1.52648566 1.52252358

17 20.00 1.00 1.00000000 1.00000000 1.00000000

18 20.00 1.00 1.00000000 1.00000000 1.00000000

THERMAL COEFFICIENT OF EXPANSION DATA:

Surf Glass TCE *10E-6

0 0.00000000

1 0.00000000

2 BALF50 8.30000000

3 0.00000000

4 BK7 7.10000000

5 SF5 8.20000000

6 0.00000000

7 N-LAK33 6.00000000

8 0.00000000

9 SF8 8.20000000

10 0.00000000

11 N-SSK8 7.20000000

12 SF11 6.10000000

13 0.00000000

14 N-BAK2 8.00000000

15 0.00000000

16 B270 8.10000000

17 0.00000000

18 0.00000000

F/# DATA:

F/# calculations consider vignetting factors and ignore surface apertures.

Wavelength: 0.450000 0.525000 0.600000

# Field Tan Sag Tan Sag Tan Sag

1 -8.3100, 0.0000 deg: 1.4283 1.4432 1.4271 1.4428 1.4289 1.4452

2 0.0000, 0.0000 deg: 1.4151 1.4151 1.4138 1.4138 1.4157 1.4157

3 8.3100, 0.0000 deg: 1.4283 1.4432 1.4271 1.4428 1.4289 1.4452

ELEMENT VOLUME DATA:

Values are only accurate for plane and spherical surfaces.

Element volumes are computed by assuming edges are squared up

to the larger of the front and back radial aperture.

Single elements that are duplicated in the Lens Data Editor

for ray tracing purposes may be listed more than once yielding

incorrect total mass estimates.

Volume cc Density g/cc Mass g

Element surf 4 to 5 45.096369 2.510000 113.191887

Element surf 5 to 6 24.578259 4.070000 100.033513

Element surf 7 to 8 34.972111 4.260000 148.981194

Element surf 9 to 10 55.886382 4.220000 235.840531

Element surf 11 to 12 76.220367 3.270000 249.240602

Element surf 12 to 13 48.394167 4.740000 229.388352

Element surf 14 to 15 21.787805 2.860000 62.313123

Element surf 16 to 17 2.648312 2.540000 6.726714

Total Mass: 1145.715915

CARDINAL POINTS:

Object space positions are measured with respect to surface 1.

Image space positions are measured with respect to the image surface.

The index in both the object space and image space is considered.

Object Space Image Space

W = 0.450000 (Primary)

Focal Length : -85.012041 85.012041

Focal Planes : -99.893520 0.079896

Principal Planes : -14.881479 -84.932144

Anti-Principal Planes : -184.905560 85.091937

Nodal Planes : -14.881479 -84.932144

Anti-Nodal Planes : -184.905560 85.091937

W = 0.525000

Focal Length : -84.945405 84.945405

Focal Planes : -98.069339 0.040917

Principal Planes : -13.123934 -84.904488

Anti-Principal Planes : -183.014745 84.986323

Nodal Planes : -13.123934 -84.904488

Anti-Nodal Planes : -183.014745 84.986323

W = 0.600000

Focal Length : -85.042818 85.042818

Focal Planes : -97.246156 0.082832

Principal Planes : -12.203338 -84.959986

Anti-Principal Planes : -182.288973 85.125649

Nodal Planes : -12.203338 -84.959986

Anti-Nodal Planes : -182.288973 85.125649

6 Appendix C: Zemax Prescription for the All-Spherical Design

A partial listing of the Zemax[8] prescription for the eight-element design consisting of all spherical surfaces is as follows.

System/Prescription Data

File : D:\FTS\optics\back end 2006\back end -- catalog lenses 13l.zmx

Title: Lens has no title.

Date : WED DEC 6 2006

GENERAL LENS DATA:

Surfaces : 20

Stop : 1

System Aperture : Entrance Pupil Diameter = 60

Glass Catalogs : Schott OLD_SCHO HIKARI SCHOTT_2000

Ray Aiming : Off

Apodization :Uniform, factor = 0.00000E+000

Effective Focal Length : 84.99885 (in air at system temperature and pressure)

Effective Focal Length : 84.99885 (in image space)

Back Focal Length : 1.078012

Total Track : 175.7139

Image Space F/# : 1.416648

Paraxial Working F/# : 1.416648

Working F/# : 1.414625

Image Space NA : 0.3328241

Object Space NA : 3e-009

Stop Radius : 30

Paraxial Image Height : 12.41514

Paraxial Magnification : 0

Entrance Pupil Diameter : 60

Entrance Pupil Position : 0

Exit Pupil Diameter : 42.01051

Exit Pupil Position : -59.43608

Field Type : Angle in degrees

Maximum Field : 8.31

Primary Wave : 0.45

Lens Units : Millimeters

Angular Magnification : 1.428214

Fields : 3

Field Type: Angle in degrees

# X-Value Y-Value Weight

1 -8.310000 0.000000 1.000000

2 0.000000 0.000000 1.000000

3 8.310000 0.000000 1.000000

Vignetting Factors

# VDX VDY VCX VCY VAN

1 0.000000 0.000000 0.000000 0.000000 0.000000

2 0.000000 0.000000 0.000000 0.000000 0.000000

3 0.000000 0.000000 0.000000 0.000000 0.000000

Wavelengths : 3

Units: Microns

# Value Weight

1 0.450000 1.000000

2 0.525000 1.000000

3 0.600000 1.000000

SURFACE DATA SUMMARY:

Surf Type Comment Radius Thickness Glass Diameter Conic

OBJ STANDARD Infinity Infinity 0 0

STO STANDARD IMAGE PLANE Infinity 25 60 0

2 STANDARD CUSTOM -90 3 BALF50 75 0

3 STANDARD -118.4694 1 75 0

4 STANDARD ROLYN 200 22.0306 122.6994 17 BK7 75 0

5 STANDARD -93.19664 3 SF5 75 0

6 STANDARD -267.7376 1 75 0

7 STANDARD CUSTOM 85 17.6261 N-LAK33 75 0

8 STANDARD 115.7795 0 75 0

9 STANDARD CUSTOM 115.7795 17.6261 N-LLF1 75 0

10 STANDARD -1042.053 18.48012 75 0

11 STANDARD CUSTOM -234.264 3 SF8 75 0

12 STANDARD 80.927 0 75 0

13 STANDARD M-G 125 LAO817 80.927 27 N-SSK8 75 0

14 STANDARD -70.712 7 SF11 75 0

15 STANDARD -275.657 1 75 0

16 STANDARD CUSTOM 45 23.6816 N-BAK2 40 0

17 STANDARD 76.19266 7 40 0

18 STANDARD ROLYN -76 12.0045 -39.85493 2.3 523586 30 0

19 STANDARD Infinity 1 30 0

IMA STANDARD Infinity 24.74494 0

SURFACE DATA DETAIL:

Surface OBJ : STANDARD

Surface STO : STANDARD IMAGE PLANE

Surface 2 : STANDARD CUSTOM

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 3 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 4 : STANDARD ROLYN 200 22.0306

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 5 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 6 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 7 : STANDARD CUSTOM

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 8 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 9 : STANDARD CUSTOM

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 10 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 11 : STANDARD CUSTOM

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 12 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 13 : STANDARD M-G 125 LAO817

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 14 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 15 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 37.5

Surface 16 : STANDARD CUSTOM

Aperture : Floating Aperture

Maximum Radius : 20

Surface 17 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 20

Surface 18 : STANDARD ROLYN -76 12.0045

Aperture : Floating Aperture

Maximum Radius : 15

Surface 19 : STANDARD

Aperture : Floating Aperture

Maximum Radius : 15

Surface IMA : STANDARD

EDGE THICKNESS DATA:

Surf X-Edge Y-Edge

STO 16.815341 16.815341

2 5.092967 5.092967

3 12.962617 12.962617

4 3.251623 3.251623

5 8.238273 8.238273

6 12.358448 12.358448

7 15.148013 15.148013

8 0.000000 0.000000

9 10.709940 10.709940

10 16.134188 16.134188

11 15.233679 15.233679

12 0.000000 0.000000

13 7.024673 7.024673

14 15.199911 15.199911

15 8.251347 8.251347

16 21.664654 21.664654

17 1.397757 1.397757

18 5.230474 5.230474

19 1.000000 1.000000

IMA 0.000000 0.000000

INDEX OF REFRACTION DATA:

Surf Glass Temp Pres 0.450000 0.525000 0.600000

0 20.00 1.00 1.00000000 1.00000000 1.00000000

1 20.00 1.00 1.00000000 1.00000000 1.00000000

2 BALF50 20.00 1.00 1.60128826 1.59330461 1.58822114

3 20.00 1.00 1.00000000 1.00000000 1.00000000

4 BK7 20.00 1.00 1.52531950 1.51986781 1.51629483

5 SF5 20.00 1.00 1.69585207 1.68066679 1.67142879

6 20.00 1.00 1.00000000 1.00000000 1.00000000

7 N-LAK33 20.00 1.00 1.76936319 1.75946138 1.75308191

8 20.00 1.00 1.00000000 1.00000000 1.00000000

9 N-LLF1 20.00 1.00 1.56116181 1.55269617 1.54740437

10 20.00 1.00 1.00000000 1.00000000 1.00000000

11 SF8 20.00 1.00 1.71347577 1.69736368 1.68759081

12 20.00 1.00 1.00000000 1.00000000 1.00000000

13 N-SSK8 20.00 1.00 1.63113017 1.62245679 1.61696192

14 SF11 20.00 1.00 1.81905382 1.79633638 1.78288949

15 20.00 1.00 1.00000000 1.00000000 1.00000000

16 N-BAK2 20.00 1.00 1.54960763 1.54340900 1.53939614

17 20.00 1.00 1.00000000 1.00000000 1.00000000

18 523586 20.00 1.00 1.53252136 1.52640242 1.52244499

19 20.00 1.00 1.00000000 1.00000000 1.00000000

20 20.00 1.00 1.00000000 1.00000000 1.00000000

THERMAL COEFFICIENT OF EXPANSION DATA:

Surf Glass TCE *10E-6

0 0.00000000

1 0.00000000

2 BALF50 8.30000000

3 0.00000000

4 BK7 7.10000000

5 SF5 8.20000000

6 0.00000000

7 N-LAK33 6.00000000

8 0.00000000

9 N-LLF1 8.00000000

10 0.00000000

11 SF8 8.20000000

12 0.00000000

13 N-SSK8 7.20000000

14 SF11 6.10000000

15 0.00000000

16 N-BAK2 8.00000000

17 0.00000000

18 523586 0.00000000

19 0.00000000

20 0.00000000

F/# DATA:

F/# calculations consider vignetting factors and ignore surface apertures.

Wavelength: 0.450000 0.525000 0.600000

# Field Tan Sag Tan Sag Tan Sag

1 -8.3100, 0.0000 deg: 1.4228 1.4150 1.4204 1.4141 1.4215 1.4160

2 0.0000, 0.0000 deg: 1.4146 1.4146 1.4120 1.4120 1.4130 1.4130

3 8.3100, 0.0000 deg: 1.4228 1.4150 1.4204 1.4141 1.4215 1.4160

ELEMENT VOLUME DATA:

Values are only accurate for plane and spherical surfaces.

Element volumes are computed by assuming edges are squared up

to the larger of the front and back radial aperture.

Single elements that are duplicated in the Lens Data Editor

for ray tracing purposes may be listed more than once yielding

incorrect total mass estimates.

Volume cc Density g/cc Mass g

Element surf 2 to 3 17.708100 3.110000 55.072190

Element surf 4 to 5 45.096369 2.510000 113.191887

Element surf 5 to 6 24.578259 4.070000 100.033513

Element surf 7 to 8 72.615583 4.260000 309.342383

Element surf 9 to 10 62.719837 2.490000 156.172394

Element surf 11 to 12 39.853108 4.220000 168.180114

Element surf 13 to 14 76.220367 3.270000 249.240602

Element surf 14 to 15 48.394167 4.740000 229.388352

Element surf 16 to 17 28.535875 2.860000 81.612602

Element surf 18 to 19 2.648312 0.000000 0.000000

Total Mass: 1462.234036

CARDINAL POINTS:

Object space positions are measured with respect to surface 1.

Image space positions are measured with respect to the image surface.

The index in both the object space and image space is considered.

Object Space Image Space

W = 0.450000 (Primary)

Focal Length : -84.998852 84.998852

Focal Planes : -121.396547 0.078012

Principal Planes : -36.397695 -84.920840

Anti-Principal Planes : -206.395399 85.076863

Nodal Planes : -36.397695 -84.920840

Anti-Nodal Planes : -206.395399 85.076863

W = 0.525000

Focal Length : -84.948873 84.948873

Focal Planes : -119.297635 0.076217

Principal Planes : -34.348762 -84.872656

Anti-Principal Planes : -204.246508 85.025090

Nodal Planes : -34.348762 -84.872656

Anti-Nodal Planes : -204.246508 85.025090

W = 0.600000

Focal Length : -85.053435 85.053435

Focal Planes : -118.322433 0.131825

Principal Planes : -33.268998 -84.921610

Anti-Principal Planes : -203.375869 85.185260

Nodal Planes : -33.268998 -84.921610

Anti-Nodal Planes : -203.375869 85.185260