Optical Effect of Flexure in Vertically Mounted Precision Mirrors

Gerhard Schwesinger

doi:10.1364/JOSA.44.000417

Journal of the Optical Society of America
Vol. 44,
Issue 5,
pp. 417-424
(1954)
•https://doi.org/10.1364/JOSA.44.000417

Optical Effect of Flexure in Vertically Mounted Precision Mirrors

Gerhard Schwesinger

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Gerhard Schwesinger, "Optical Effect of Flexure in Vertically Mounted Precision Mirrors," J. Opt. Soc. Am. 44, 417-424 (1954)

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

Abstract

Under their own weight, large concave mirrors, such as used in telescopes and various research equipment, may elastically bend beyond tolerable limits. The problem of preventing harmful mirror deformations arises in full severity when gravity has a substantial component in the direction of the optical axis. The less serious case of gravity acting perpendicular to the optical axis has been dismissed by one author as harmless for mirror sizes up to 120 inches. However, disfigurations observed on much smaller vertically mounted mirrors are definitely traceable to elastic flexure by gravity. This paper briefly discusses the elastic deformation of an upright solid disk with a concave front surface and a plane back, supported along its edge by a distribution of radial forces which originate in the contact areas between disk and mount. The loss of image definition through flexure is related to the Fourier coefficients of the edge-pressure distribution in an explicit form simple enough as to permit the analysis of various types of mounts, as well as the synthesis of optimum mounting conditions. Numerical values and graphs are presented from which the optical effect can be appraised for different mirror shapes. The results are compared with observations made in practical tests.

Full Article | PDF Article

More Like This

Adjustable bipod flexures for mounting mirrors in a space telescope

Hagyong Kihm, Ho-Soon Yang, Il Kweon Moon, Jeong-Heum Yeon, Seung-Hoon Lee, and Yun-Woo Lee
Appl. Opt. 51(32) 7776-7783 (2012)

Adjustable flexure mount to compensate for deformation of an optic surface

Zhou Feng, Yu Jie, Wang Li-Ping, Li Yuan-Ming, Zhang Hai-Tao, Man Quan, Li Qiang, Bi Ran, Wang Hui, and Jin Chun-Shui
Appl. Opt. 58(34) 9370-9375 (2019)

Design and optimization of integrated flexure mounts for unloading lateral gravity of a lightweight mirror for space application

Liu Zhang, Tailei Wang, Fan Zhang, Huanyu Zhao, Yu Zhao, and Xiaoyi Zheng
Appl. Opt. 60(2) 417-426 (2021)

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 (7)

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 (4)

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

Mode n	ρ = 0	0.2	0.4	0.6	0.8	1.0
0	−0.02332	−0.01780	−0.00428	0.00883	0.00830	−0.02157
1	0	−0.00289	−0.00273	0.00079	0.00312	−0.00667
2	0	0.0140	0.0545	0.1167	0.1917	0.2640
3		0.0014	0.0108	0.0339	0.0707	0.1118
4		0.0002	0.0033	0.0154	0.0425	0.0821
5			0.0012	0.0081	0.0298	0.0724
6			0.0004	0.0045	0.0222	0.0681
7			0.0002	0.0026	0.0170	0.0657
8			0.0001	0.0015	0.0132	0.0643
9				0.0009	0.0103	0.0633
10				0.0005	0.0081	0.0624

Aberration	$s_{max} / \bar{s}$
Primary spherical aberration^a	$3 {(5)}^{\frac{1}{2}} / 2 = 3.354$
Zonal spherical aberration^b	$2 {(7)}^{\frac{1}{2}} = 5.292$
Primary astigmatism^c	$2 {(6)}^{\frac{1}{2}} = 4.899$
Primary coma^c,^d	$3 {(8)}^{\frac{1}{2}} / 2 = 4.243$
Sinusoidal wave aberration	$2 {(2)}^{\frac{1}{2}} = 2.828$
Out-of-focus image	$2 {(3)}^{\frac{1}{2}} = 3.464$

Mode n	κ = 0	0.1	0.2	0.3
0	0	1.01	4.04	9.1
1	0	0.0331	0.132	0.30
2	4.59	140.5	465.	978.
3	3.45	20.7	52.5	99.
4	2.76	8.89	18.5	32.
5	2.30	5.49	10.1	16.
6	1.97	3.92	6.55	9.9
7	1.72	3.06	4.79	6.9
8	1.53	2.53	3.79	5.3
9	1.38	2.18	3.17	4.3
10	1.25	1.92	2.74	3.7

Case	Type of support	κ = 0	0.1	0.2	0.3
a	Ideal support	0	0.0018	0.0036	0.0055
b	Prestressed elastic lining	0	0.0132	0.0289	0.0464
c	Unstressed elastic lining.	0.00920	0.0508	0.0926	0.1350
d	Belt-type suspension	0.00743	0.0182	0.0301	0.0421
e	V support, ∊ = 45°	0.0548	0.0832	0.1152	0.148
e	On-edge-support, ∊ = 0	0.0673	0.148	0.246	0.346

Mode n	ρ = 0	0.2	0.4	0.6	0.8	1.0
0	−0.02332	−0.01780	−0.00428	0.00883	0.00830	−0.02157
1	0	−0.00289	−0.00273	0.00079	0.00312	−0.00667
2	0	0.0140	0.0545	0.1167	0.1917	0.2640
3		0.0014	0.0108	0.0339	0.0707	0.1118
4		0.0002	0.0033	0.0154	0.0425	0.0821
5			0.0012	0.0081	0.0298	0.0724
6			0.0004	0.0045	0.0222	0.0681
7			0.0002	0.0026	0.0170	0.0657
8			0.0001	0.0015	0.0132	0.0643
9				0.0009	0.0103	0.0633
10				0.0005	0.0081	0.0624

Abstract

Cited By

Figures (7)

Tables (4)

Equations (41)

Journal of the Optical Society of America