Stressed mirror polishing. 2: Fabrication of an off-axis section of a paraboloid

Jerry E. Nelson; George Gabor; Leslie K. Hunt; Jacob Lubliner; Terry S. Mast

doi:10.1364/AO.19.002341

Applied Optics
Vol. 19,
Issue 14,
pp. 2341-2352
(1980)
•https://doi.org/10.1364/AO.19.002341

Stressed mirror polishing. 2: Fabrication of an off-axis section of a paraboloid

Jerry E. Nelson, George Gabor, Leslie K. Hunt, Jacob Lubliner, and Terry S. Mast

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Jerry E. Nelson, George Gabor, Leslie K. Hunt, Jacob Lubliner, and Terry S. Mast, "Stressed mirror polishing. 2: Fabrication of an off-axis section of a paraboloid," Appl. Opt. 19, 2341-2352 (1980)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

A mirror has been fabricated with the shape of an off-axis section of a paraboloid by grinding and polishing a sphere into a prestressed blank. The applied stresses were then removed allowing the mirror to spring into the desired paraboloidal shape. The 36-cm diam off-axis section deviated 9.9-μm rms from the polished sphere. The final surface deviated 0.03-μm rms from the desired off-axis section.

Full Article | PDF Article

More Like This

Stressed mirror polishing. 1: A technique for producing nonaxisymmetric mirrors

Jacob Lubliner and Jerry E. Nelson
Appl. Opt. 19(14) 2332-2340 (1980)

Influence and control of spherical aberration in polishing off-axis aspherical mirrors by the stressed method

Jiang Zi Bo, Li Xin Nan, Yu Bin Bin, Zheng Yi, and Li Bo
Appl. Opt. 54(2) 291-298 (2015)

Comprehensive study of the rapid stressed mirror polishing method for off-axis aspheric SiC thin-plate mirrors

Liqi Yi, Xuejun Zhang, Haifei Hu, Zhiyu Zhang, Kuo Hai, Xiao Luo, and Donglin Xue
Opt. Express 28(22) 32802-32818 (2020)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (8)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (41)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

					Zernike Coefficients (μ m
n	m	^Znm(ρ,θ)	Cylindrical Monomial Coefficient Relationship	Weight	Desired Deflections	Desired Parabola	First* Polish	Second* Polish	Measured Residuals from Best Fitting Paraboloid

0	0	1	$C_{00} = α_{00} + \frac{α_{20}}{2} + \frac{α_{40}}{3} + . . .$	1
1	−1	ρsinθ	$C_{1 - 1} = α_{1 - 1} + \frac{2}{3} α_{3 - 1} + . . .$	$\frac{1}{4}$		$[\begin{matrix} k = 368.80 cm \\ R = 35.00 cm \\ ϕ = 0.0 \end{matrix}]$	$[\begin{array}{l} k = 368.68 cm \\ R = 35.79 cm \\ ϕ = 0.0043 \end{array}]$	$[\begin{array}{l} k = 368.83 cm \\ R = 35.07 cm \\ ϕ = 0.0060 \end{array}]$
1	1	ρcosθ	$C_{11} = α_{11} + \frac{2}{3} α_{31} + . . .$	$\frac{1}{4}$
2	−2	ρ²sin2θ	$C_{2 - 2} = α_{2 - 2} + \frac{3}{4} α_{4 - 2} + . . .$	$\frac{1}{6}$	0.00	0.00	−0.15	0.24	0.02
2	0	2ρ² − 1	$C_{20} = \frac{α_{20}}{2} + \frac{α_{40}}{2} + . . .$	$\frac{1}{3}$	−8.93	2161.88	2162.59	2161.68	0.00
2	2	ρ²cos2θ	$C_{22} = α_{22} + \frac{3}{4} α_{42} + . . .$	$\frac{1}{6}$	19.34	−19.34	−20.21	−19.42	−0.02
3	−3	ρ³sin3θ	C₃₋₃ = α₃₋₃ + …	$\frac{1}{8}$	0.00	0.00	0.02	0.02	0.01
3	−1	(3ρ³ − 2ρ)sinθ	$C_{3 - 1} = \frac{α_{3 - 1}}{3} + . . .$	$\frac{1}{8}$	0.00	0.00	−0.16	−0.01	−0.05
3	1	(3ρ³ − 2ρ) cosθ	$C_{31} = \frac{α_{31}}{3} + . . .$	$\frac{1}{8}$	6.55	−6.55	−6.71	−6.55	0.01
3	3	ρ³ cos3θ	C₃₃ = α₃₃+…	$\frac{1}{8}$	−0.04	0.04	0.00	0.00	−0.04
4	−4	ρ⁴ sin4θ	C₄₋₄ = α₄₋₄+…	$\frac{1}{10}$	0.00	0.00	0.02	0.02	0.03
4	−2	(4ρ⁴ − 3ρ²) sin2θ	$C_{4 - 2} = \frac{α_{4 - 2}}{4} + . . .$	$\frac{1}{10}$	0.00	0.00	0.02	0.00	0.00
4	0	6ρ⁴ − 6ρ² + 1	$C_{40} = \frac{α_{40}}{6} + . . .$	$\frac{1}{5}$	0.40	0.01	−0.11	0.04	0.03
4	2	(4ρ⁴ − 3ρ²) cos2θ	$C_{42} = \frac{α_{42}}{4} + . . .$	$\frac{1}{10}$	−0.01	0.01	−0.07	0.02	0.00
4	4	ρ⁴ cos4θ	C₄₄ = α₄₄+…	$\frac{1}{10}$	0.00	0.00	−0.01	0.04	0.05
					(Z − Z_desired)_rms		0.55	0.16
					(Z − Z_best) _rms		0.08	0.03

		First Polish		Second Polish
Angle	Lever No.	Force, kg	Couple, kg–cm	Force, kg	Couple, kg–cm
15°	1	−16.78	260.38	−15.75	246.56
30°	2	−17.73	213.92	−16.76	204.70
45°	3	−18.73	144.59	−17.74	141.79
60°	4	−19.07	62.68	−18.13	65.98
75°	5	−18.06	−20.54	−17.28	−13.00
90°	6	−15.29	−95.13	−14.62	−85.56
105°	7	−10.73	−154.32	−9.98	−144.65
120°	8	−4.86	−195.48	−3.88	−187.35
135°	9	1.46	−219.94	2.58	−214.84
150°	10	7.11	−231.82	8.13	−230.66
165°	11	11.03	−236.22	11.73	−238.43
180°	12	12.43	−237.17	12.84	−240.42
195°	13	11.03	−236.22	11.39	−237.21
210°	14	7.11	−2 31.82	7.65	−228.03
225°	15	1.46	−219.94	2.16	−211.07
240°	16	−4.86	−195.48	−4.19	−183.51
255°	17	−10.73	−154.32	−10.26	−142.20
270°	18	−15.29	−95.13	−14.92	−85.27
285°	19	−18.06	−20.54	−17.48	−14.22
300°	20	−19.07	62.68	−17.98	64.86
315°	21	−18.73	144.59	−17.14	142.06
330°	22	−17.73	213.92	−15.93	206.20
345°	23	−16.78	260.38	−15.14	247.96
360°	24	−16.40	276.73	−15.11	261.82

					Zernike Coefficients (μ m
n	m	^Znm(ρ,θ)	Cylindrical Monomial Coefficient Relationship	Weight	Desired Deflections	Desired Parabola	First* Polish	Second* Polish	Measured Residuals from Best Fitting Paraboloid

0	0	1	$C_{00} = α_{00} + \frac{α_{20}}{2} + \frac{α_{40}}{3} + . . .$	1
1	−1	ρsinθ	$C_{1 - 1} = α_{1 - 1} + \frac{2}{3} α_{3 - 1} + . . .$	$\frac{1}{4}$		$[\begin{matrix} k = 368.80 cm \\ R = 35.00 cm \\ ϕ = 0.0 \end{matrix}]$	$[\begin{array}{l} k = 368.68 cm \\ R = 35.79 cm \\ ϕ = 0.0043 \end{array}]$	$[\begin{array}{l} k = 368.83 cm \\ R = 35.07 cm \\ ϕ = 0.0060 \end{array}]$
1	1	ρcosθ	$C_{11} = α_{11} + \frac{2}{3} α_{31} + . . .$	$\frac{1}{4}$
2	−2	ρ²sin2θ	$C_{2 - 2} = α_{2 - 2} + \frac{3}{4} α_{4 - 2} + . . .$	$\frac{1}{6}$	0.00	0.00	−0.15	0.24	0.02
2	0	2ρ² − 1	$C_{20} = \frac{α_{20}}{2} + \frac{α_{40}}{2} + . . .$	$\frac{1}{3}$	−8.93	2161.88	2162.59	2161.68	0.00
2	2	ρ²cos2θ	$C_{22} = α_{22} + \frac{3}{4} α_{42} + . . .$	$\frac{1}{6}$	19.34	−19.34	−20.21	−19.42	−0.02
3	−3	ρ³sin3θ	C₃₋₃ = α₃₋₃ + …	$\frac{1}{8}$	0.00	0.00	0.02	0.02	0.01
3	−1	(3ρ³ − 2ρ)sinθ	$C_{3 - 1} = \frac{α_{3 - 1}}{3} + . . .$	$\frac{1}{8}$	0.00	0.00	−0.16	−0.01	−0.05
3	1	(3ρ³ − 2ρ) cosθ	$C_{31} = \frac{α_{31}}{3} + . . .$	$\frac{1}{8}$	6.55	−6.55	−6.71	−6.55	0.01
3	3	ρ³ cos3θ	C₃₃ = α₃₃+…	$\frac{1}{8}$	−0.04	0.04	0.00	0.00	−0.04
4	−4	ρ⁴ sin4θ	C₄₋₄ = α₄₋₄+…	$\frac{1}{10}$	0.00	0.00	0.02	0.02	0.03
4	−2	(4ρ⁴ − 3ρ²) sin2θ	$C_{4 - 2} = \frac{α_{4 - 2}}{4} + . . .$	$\frac{1}{10}$	0.00	0.00	0.02	0.00	0.00
4	0	6ρ⁴ − 6ρ² + 1	$C_{40} = \frac{α_{40}}{6} + . . .$	$\frac{1}{5}$	0.40	0.01	−0.11	0.04	0.03
4	2	(4ρ⁴ − 3ρ²) cos2θ	$C_{42} = \frac{α_{42}}{4} + . . .$	$\frac{1}{10}$	−0.01	0.01	−0.07	0.02	0.00
4	4	ρ⁴ cos4θ	C₄₄ = α₄₄+…	$\frac{1}{10}$	0.00	0.00	−0.01	0.04	0.05
					(Z − Z_desired)_rms		0.55	0.16
					(Z − Z_best) _rms		0.08	0.03

		First Polish		Second Polish
Angle	Lever No.	Force, kg	Couple, kg–cm	Force, kg	Couple, kg–cm
15°	1	−16.78	260.38	−15.75	246.56
30°	2	−17.73	213.92	−16.76	204.70
45°	3	−18.73	144.59	−17.74	141.79
60°	4	−19.07	62.68	−18.13	65.98
75°	5	−18.06	−20.54	−17.28	−13.00
90°	6	−15.29	−95.13	−14.62	−85.56
105°	7	−10.73	−154.32	−9.98	−144.65
120°	8	−4.86	−195.48	−3.88	−187.35
135°	9	1.46	−219.94	2.58	−214.84
150°	10	7.11	−231.82	8.13	−230.66
165°	11	11.03	−236.22	11.73	−238.43
180°	12	12.43	−237.17	12.84	−240.42
195°	13	11.03	−236.22	11.39	−237.21
210°	14	7.11	−2 31.82	7.65	−228.03
225°	15	1.46	−219.94	2.16	−211.07
240°	16	−4.86	−195.48	−4.19	−183.51
255°	17	−10.73	−154.32	−10.26	−142.20
270°	18	−15.29	−95.13	−14.92	−85.27
285°	19	−18.06	−20.54	−17.48	−14.22
300°	20	−19.07	62.68	−17.98	64.86
315°	21	−18.73	144.59	−17.14	142.06
330°	22	−17.73	213.92	−15.93	206.20
345°	23	−16.78	260.38	−15.14	247.96
360°	24	−16.40	276.73	−15.11	261.82

Abstract

Cited By

Figures (8)

Tables (2)

Equations (41)

Applied Optics