Least-squares fitting of aspheric surfaces by a conicoid

Berge Tatian

doi:10.1364/AO.28.004687

Applied Optics
Vol. 28,
Issue 21,
pp. 4687-4696
(1989)
•https://doi.org/10.1364/AO.28.004687

Least-squares fitting of aspheric surfaces by a conicoid

Berge Tatian

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Berge Tatian, "Least-squares fitting of aspheric surfaces by a conicoid," Appl. Opt. 28, 4687-4696 (1989)

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Abstract

Spherical fits to an aspheric surface provide a measure of the raw asphericity, give an easily generated starting point for its fabrication, and show the amount of aberration to be expected in a center of curvature test. Conicoidal fits have similar uses. We have previously shown that a conicoidal fit can be substantially closer than a spherical fit. In this paper we include fits to sections of plane symmetric surfaces that have no symmetry and give examples of such fits to surfaces of a completely asymmetric lens.

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CURV	3.79E+07
CC	2.76E+05
AST	3.87E+04
AST ROT	3.59E+04
BETA	2.38E+04
ALPHA	1.78E+03
YD	1.91E+00
GAMMA	7.96E-03
ZD	4.95E-05

SN=1	PLANO	TH = 3.810000E+03	DUMMY
SN=2	PLANO	TH −2.133600E+03	DUMMY
SN=2	SURF TILT	AL = −5.369480E−01	BE = −1.454254E−01	GA= −2.216883E−01
SN=3	UNUSUAL	TH = 0.0	REFLECTION
	SURF DEC.	XD = 1.390712E+02	YD = −5.999336E+02
	SURF TILT	AL = 2.609764E−01	BE = −2.199842E−01	GA= −1.306520E+00
SN=4	PLANO	TH = −2.492778E+03	DUMMY
	AXIS DEC	XD = 4.484096E+02	YD = −1.102290E+03
	AXIS TILT	AL = −2.890962E−01	BE = −1.549275E−01	GA= −1.259563E+00
SN=5	UNUSUAL	TH = 2.467348E+03	REFLECTION	STOP
	SURF DEC.	XD = 2.115794E+02	YD = 3.361089E+01
	SURF TILT	AL = 7.845601E−02	BT = −2.330287E−02	GA=4.767971E−02
SN=6	UNUSUAL	TH = −2.425114E+03	REFLECTION
	SURF DEC.	XD = −1.311503E+02	YD = 1.436986E+02
	SURF TILT	AL = −4.634113E−02	BE = −1.183955E−01	GA=8.038125E−04
	AXIS TILT	AL = 1.471043E−01	BE = −2.250445E−03
SN=7	SPHERE	CV = −2.266640E−04	TH = −2.540000E+01	GERMANIUM
SN=7	AXIS DEC.	XD = 9.990755E+02	YD = 4.099096E+02
SN=8	PLANO	TH = −2.548439E+01
SN=9	PLANO IMAGE

	SN=3	SN=5	SN=6
CX	2.712257E−06	−2.097548E−04	−3.011253E−04
CY	−3.220349E−06	−1.731069E−04	−2.894523E−04
CZ	0.0	1.245720E−04	−3.396323E−04
X0	0.0	5.514439E+01	2.138443E+02
Y0	0.0	3.055100E+02	−3.850215E+02
U4	−1.929238E−12	−4.733836E−11	−2.125548E−12
U6	9.228008E−21	9.534171E−18	1.143584E−19
Y3	−5.759325E−11	−1.706314E−08	2.009716E−09
X2Y	−1.618161E−09	−2.823540E−08	1.551347E−09
Y4	4.269474E−13	8.695738E−12	1.042650E−12
X2Y2	−2.073793E−12	2.122201E−11	2.025589E−12
X4	8.024886E−13	1.145516E−11	9.806559E−13
Y5	−3.161027E−16	−1.875699E−15	1.039893E−16
X2Y3	−5.710027E−16	−5.564113E−15	2.028146E−16
X4Y	−1.724073E−16	−3.968850E−15	9.262333E−17
Y6	−5.217036E−20	−8.788063E−19	3.702759E−20
X2Y4	−1.568117E−19	−7.141793E−18	1.194800E−19
X4Y2	−1.232100E−19	−8.080210E−18	1.205667E−19
X6	−2.621066E−20	−3.200138E−18	4.218637E−20

SN	X	Y	Z	K	L
0				0.00000000	0.00000000
0				0.00000000	0.00000000
1	2542.5270	− 711.8883	0.0000	0.00000000	0.00000000
1	2542.5270	− 711.8883	0.0000	0.00000000	0.00000000
2	2542.5270	−711.8883	0.0000	0.00000000	0.00000000
2	2542.5270	− 711.8883	3810.0000	0.00000000	0.00000000
3	− 491.6495	− 1190.0502	− 2.0994	− 0.27882674	0.21233578
3	2542.5270	− 711.8882	2185.9415	− 0.38918258	− 0.54007443
4	− 299.0134	− 735.4730	0.0000	− 0.19208068	− 0.28932281
4	2316.2450	− 1025.9033	2619.8202	− 0.38918258	− 0.54007443
5	− 0.0000	− 0.0000	− 0.0000	0.22920318	0.17626210
5	3350.7782	409.7338	636.1810	− 0.78157442	− 0.01881230
6.	1131.1582	236.8465	− 159.5044	0.19458720	0.10860005
6.	1362.6557	361.8802	2222.2751	− 0.68058480	− 0.20596103
7	0.3277	0.0783	− 0.0000	0.00066938	− 0.00127347
7	3060.3378	875.6388	468.3684	− 0.68336246	− 0.20724243
8	0.3107	0.1106	0.0000	0.00271226	− 0.00516000
8	3077.6952	880.9028	450.5872	− 0.68063629	− 0.20573430
9	0.2416	0.2421	0.0000	0.00271226	− 0.00516000
9	3095.0411	886.1459	432.6677	− 0.68063629	− 0.20573430
	K/M	L/M	XDIST	YDIST
	0.0027123	− 0.0051601	0.2416091	0.2421104

CURV	3.79E+07
CC	2.76E+05
AST	3.87E+04
AST ROT	3.59E+04
BETA	2.38E+04
ALPHA	1.78E+03
YD	1.91E+00
GAMMA	7.96E-03
ZD	4.95E-05

Abstract

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Figures (16)

Tables (4)

Equations (10)

Applied Optics