Adaptive frequency comb illumination for interferometry in the case of nested two-beam cavities

Irina Harder; Gerd Leuchs; Klaus Mantel; Johannes Schwider

doi:10.1364/AO.50.004942

Applied Optics
Vol. 50,
Issue 25,
pp. 4942-4956
(2011)
•https://doi.org/10.1364/AO.50.004942

Adaptive frequency comb illumination for interferometry in the case of nested two-beam cavities

Irina Harder, Gerd Leuchs, Klaus Mantel, and Johannes Schwider

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Irina Harder, Gerd Leuchs, Klaus Mantel, and Johannes Schwider, "Adaptive frequency comb illumination for interferometry in the case of nested two-beam cavities," Appl. Opt. 50, 4942-4956 (2011)

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

Abstract

The homogeneity test of glass plates in a Fizeau interferometer is hampered by the superposition of multiple interference signals coming from the surfaces of the glass plate as well as the empty Fizeau cavity. To evaluate interferograms resulting from such nested cavities, various approaches such as the use of broadband light sources have been applied. In this paper, we propose an adaptive frequency comb interferometer to accomplish the cavity selection. An adjustable Fabry–Perot resonator is used to generate a variable frequency comb that can be matched to the length of the desired cavity. Owing to its flexibility, the number of measurements needed for the homogeneity test can be reduced to four. Furthermore, compared to approaches using a two-beam interferometer as a filter for the broadband light source, the visibility of the fringe system is considerably higher if a Fabry–Perot filter is applied.

Full Article | PDF Article

More Like This

Interferometric homogeneity test using adaptive frequency comb illumination

Klaus Mantel and Johannes Schwider
Appl. Opt. 52(9) 1897-1912 (2013)

50 years of optics research [Invited]

Johannes Schwider
Appl. Opt. 52(1) 9-19 (2013)

Superposition fringes as a measuring tool in optical testing

J. Schwider
Appl. Opt. 18(14) 2364-2367 (1979)

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 (15)

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 (3)

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 (27)

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

Optical cavity length	FP filter cavity/mm
$t_{1}$	$1.358 \pm 0.005$
${N t}_{2}$	$17.366 \pm 0.005$
$t_{3}$	$2.3065 \pm 0.005$
$t_{4}$	$14.992 \pm 0.005$
$t_{1} + {N t}_{2} + t_{3}$	$21.019 \pm 0.005$
${N t}_{2} + t_{3}$	$19.667 \pm 0.005$
$t_{1} + {N t}_{2}$	$18.717 \pm 0.005$

Combination $1 / 2$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R) \cos (φ_{2} - φ_{1})]$	$V = \frac{2 (1 - R)}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.92}{3.5535} = 0.54$
Combination $1 / 3$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{2} \cos (φ_{3} - φ_{1})]$	$V = \frac{2 (1 - R)^{2}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.843}{3.5535} = 0.518$
Combination $2 / 3$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{3} \cos (φ_{3} - φ_{2})]$	$V = \frac{2 (1 - R)^{3}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.769}{3.5535} = 0.498$
Combination $1 / 4$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{3} \cos (φ_{4} - φ_{1})]$	$V = \frac{2 (1 - R)^{3}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.769}{3.5535} = 0.498$
Combination $3 / 4$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{5} \cos (φ_{4} - φ_{3})]$	$V = \frac{2 (1 - R)^{5}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.631}{3.5535} = 0.456$

Surfaces $2 / 3$	$I = \| u_{0} \|^{2} R (1 - R)^{2} [1 + (1 - R)^{2} + 2 (1 - R) \cos (φ_{3} - φ_{2})]$	$V = \frac{2 (1 - R)}{1 + (1 - R)^{2}} = 0.999$
Surfaces $1 / 4$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{6} + 2 (1 - R)^{3} \cos (φ_{4} - φ_{1})]$	$V = \frac{2 (1 - R)^{3}}{1 + (1 - R)^{6}} = 0.992$

Optical cavity length	FP filter cavity/mm
$t_{1}$	$1.358 \pm 0.005$
${N t}_{2}$	$17.366 \pm 0.005$
$t_{3}$	$2.3065 \pm 0.005$
$t_{4}$	$14.992 \pm 0.005$
$t_{1} + {N t}_{2} + t_{3}$	$21.019 \pm 0.005$
${N t}_{2} + t_{3}$	$19.667 \pm 0.005$
$t_{1} + {N t}_{2}$	$18.717 \pm 0.005$

Combination $1 / 2$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R) \cos (φ_{2} - φ_{1})]$	$V = \frac{2 (1 - R)}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.92}{3.5535} = 0.54$
Combination $1 / 3$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{2} \cos (φ_{3} - φ_{1})]$	$V = \frac{2 (1 - R)^{2}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.843}{3.5535} = 0.518$
Combination $2 / 3$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{3} \cos (φ_{3} - φ_{2})]$	$V = \frac{2 (1 - R)^{3}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.769}{3.5535} = 0.498$
Combination $1 / 4$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{3} \cos (φ_{4} - φ_{1})]$	$V = \frac{2 (1 - R)^{3}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.769}{3.5535} = 0.498$
Combination $3 / 4$	$I = \| u_{0} \|^{2} R [1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6} + 2 (1 - R)^{5} \cos (φ_{4} - φ_{3})]$	$V = \frac{2 (1 - R)^{5}}{1 + (1 - R)^{2} + (1 - R)^{4} + (1 - R)^{6}} = \frac{1.631}{3.5535} = 0.456$

Abstract

Cited By

Figures (15)

Tables (3)

Equations (27)

Applied Optics