Abstract

A single-arm off-axis holographic interferometer (SA-OHI) system for visual inspection of the three-dimensional (3-D) surfaces and refractive-index profiles of micrometer-scale optical lenses is proposed. In this system, a couple of pellicle beam splitters and optical mirrors are employed to generate two sheared off-axis beams from the single object beam by controlling the tilted angle of the optical mirror. Each sheared beam is divided into two areas with and without object data, which are called half-object and half-reference beams, respectively. These sub-divided object and reference beams then make interference patterns, just like the conventional two-arm holographic interferometer. This holographic interferometer system, called SA-OHI, can solve the DC bias, virtual and duplicated image problems occurred in most lateral shearing interferometers, which allow extraction of the hologram data only related to the target object. The operational principle of the proposed system is analyzed based on ray-optics. To confirm the feasibility of the proposed system in the practical application fields, experiments with test lenses are also carried out and the results are comparatively discussed with those of the conventional system.

© 2016 Optical Society of America

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References

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2015 (3)

C.-W. Liu, C.-C. Wu, and S.-C. Lin, “A simple and wide-range refractive index measuring approach by using a sub-microngrating,” Appl. Phys. Lett. 106(15), 151907 (2015).
[Crossref]

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54(5), 054105 (2015).
[Crossref]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

2014 (2)

K.-B. Seo, B.-M. Kim, and E.-S. Kim, “Digital holographic microscopy based on a modified lateral shearing interferometer for three-dimensional visual inspection of nanoscale defects on transparent objects,” Nanoscale Res. Lett. 9(1), 471 (2014).
[Crossref] [PubMed]

S. Shin and Y. Yu, “Determining the Refractive Index and Three-Dimensional Shape of an Optical Component using Digital Holographic Microscopy with Liquid,” Korean J. Opt. Photon. 25(3), 137–141 (2014).
[Crossref]

2012 (1)

M. Agour, P. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using slm-based phase retrieval and a phase diffuser,” J. Eur. Opt. Soc. 7, 12046 (2012).
[Crossref]

2009 (1)

2005 (1)

2004 (1)

2003 (2)

I. Bányász, “Direct measurement of the refractive index profile of phase gratings, recorded in silver halide holographic materials by phase-contrast microscopy,” Appl. Phys. Lett. 83(21), 4282–4284 (2003).
[Crossref]

S. M. Baumer, L. Shulepova, J. Willemse, and K. Renkmena, “Integral optical system design of injection molded optics,” Proc. SPIE 5173, 38–45 (2003).
[Crossref]

1996 (2)

M. F. M. Costa, “Surface inspection by an optical triangulation method,” Opt. Eng. 35(9), 2743–2747 (1996).
[Crossref]

G. S. Sarkisov, “Shearing interferometer with an air wedge for electron density diagnostics in a dense plasma,” Instrum. Exp. Tech. 39, 727–731 (1996).

1995 (2)

S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118(5-6), 491–494 (1995).
[Crossref]

J. Choi, G. M. Perera, M. D. Aggarwal, R. P. Shukla, and M. V. Mantravadi, “Wedge-plate shearing interferometers for collimation testing: use of a moiré technique,” Appl. Opt. 34(19), 3628–3638 (1995).
[Crossref] [PubMed]

1991 (1)

T. A. Clarke, K. T. V. Grattan, and N. E. Lindsey, “Laser-based triangulation techniques in optical inspection of industrial structures,” Proc. SPIE 1332, 474–486 (1991).
[Crossref]

1985 (1)

1982 (1)

1974 (1)

1973 (1)

1966 (1)

Aggarwal, M. D.

Agour, M.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

M. Agour, P. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using slm-based phase retrieval and a phase diffuser,” J. Eur. Opt. Soc. 7, 12046 (2012).
[Crossref]

Almoro, P.

M. Agour, P. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using slm-based phase retrieval and a phase diffuser,” J. Eur. Opt. Soc. 7, 12046 (2012).
[Crossref]

Bányász, I.

I. Bányász, “Direct measurement of the refractive index profile of phase gratings, recorded in silver halide holographic materials by phase-contrast microscopy,” Appl. Phys. Lett. 83(21), 4282–4284 (2003).
[Crossref]

Baumer, S. M.

S. M. Baumer, L. Shulepova, J. Willemse, and K. Renkmena, “Integral optical system design of injection molded optics,” Proc. SPIE 5173, 38–45 (2003).
[Crossref]

Bergmann, R. B.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54(5), 054105 (2015).
[Crossref]

Chen, Q.

Choi, J.

Clarke, T. A.

T. A. Clarke, K. T. V. Grattan, and N. E. Lindsey, “Laser-based triangulation techniques in optical inspection of industrial structures,” Proc. SPIE 1332, 474–486 (1991).
[Crossref]

Costa, M. F. M.

M. F. M. Costa, “Surface inspection by an optical triangulation method,” Opt. Eng. 35(9), 2743–2747 (1996).
[Crossref]

Dong, X.

Eiju, T.

Falldorf, C.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54(5), 054105 (2015).
[Crossref]

M. Agour, P. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using slm-based phase retrieval and a phase diffuser,” J. Eur. Opt. Soc. 7, 12046 (2012).
[Crossref]

C. Falldorf, S. Osten, C. V. Kopylow, and W. Jüptner, “Shearing interferometer based on the birefringent properties of a spatial light modulator,” Opt. Lett. 34(18), 2727–2729 (2009).
[Crossref] [PubMed]

Ferraro, P.

S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118(5-6), 491–494 (1995).
[Crossref]

Finizo, A.

S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118(5-6), 491–494 (1995).
[Crossref]

Grattan, K. T. V.

T. A. Clarke, K. T. V. Grattan, and N. E. Lindsey, “Laser-based triangulation techniques in optical inspection of industrial structures,” Proc. SPIE 1332, 474–486 (1991).
[Crossref]

Jerke, J. M.

Jüptner, W.

Kim, B.-M.

K.-B. Seo, B.-M. Kim, and E.-S. Kim, “Digital holographic microscopy based on a modified lateral shearing interferometer for three-dimensional visual inspection of nanoscale defects on transparent objects,” Nanoscale Res. Lett. 9(1), 471 (2014).
[Crossref] [PubMed]

Kim, E.-S.

K.-B. Seo, B.-M. Kim, and E.-S. Kim, “Digital holographic microscopy based on a modified lateral shearing interferometer for three-dimensional visual inspection of nanoscale defects on transparent objects,” Nanoscale Res. Lett. 9(1), 471 (2014).
[Crossref] [PubMed]

Kim, M. K.

Klattenhoff, R.

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54(5), 054105 (2015).
[Crossref]

Kopylow, C. V.

Lin, S.-C.

C.-W. Liu, C.-C. Wu, and S.-C. Lin, “A simple and wide-range refractive index measuring approach by using a sub-microngrating,” Appl. Phys. Lett. 106(15), 151907 (2015).
[Crossref]

Lindsey, N. E.

T. A. Clarke, K. T. V. Grattan, and N. E. Lindsey, “Laser-based triangulation techniques in optical inspection of industrial structures,” Proc. SPIE 1332, 474–486 (1991).
[Crossref]

Liu, C.-W.

C.-W. Liu, C.-C. Wu, and S.-C. Lin, “A simple and wide-range refractive index measuring approach by using a sub-microngrating,” Appl. Phys. Lett. 106(15), 151907 (2015).
[Crossref]

Liu, Z.

Mantravadi, M. V.

Matsuda, K.

Merzkirch, W.

Nicola, S. D.

S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118(5-6), 491–494 (1995).
[Crossref]

Nyyssonen, D.

Osten, S.

Perera, G. M.

Pesce, G.

S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118(5-6), 491–494 (1995).
[Crossref]

Pierattini, G.

S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118(5-6), 491–494 (1995).
[Crossref]

Puntambekar, P. N.

Renkmena, K.

S. M. Baumer, L. Shulepova, J. Willemse, and K. Renkmena, “Integral optical system design of injection molded optics,” Proc. SPIE 5173, 38–45 (2003).
[Crossref]

Sarkisov, G. S.

G. S. Sarkisov, “Shearing interferometer with an air wedge for electron density diagnostics in a dense plasma,” Instrum. Exp. Tech. 39, 727–731 (1996).

Sen, D.

Seo, K.-B.

K.-B. Seo, B.-M. Kim, and E.-S. Kim, “Digital holographic microscopy based on a modified lateral shearing interferometer for three-dimensional visual inspection of nanoscale defects on transparent objects,” Nanoscale Res. Lett. 9(1), 471 (2014).
[Crossref] [PubMed]

Shin, S.

S. Shin and Y. Yu, “Determining the Refractive Index and Three-Dimensional Shape of an Optical Component using Digital Holographic Microscopy with Liquid,” Korean J. Opt. Photon. 25(3), 137–141 (2014).
[Crossref]

Shukla, R. P.

Shulepova, L.

S. M. Baumer, L. Shulepova, J. Willemse, and K. Renkmena, “Integral optical system design of injection molded optics,” Proc. SPIE 5173, 38–45 (2003).
[Crossref]

Smith, G.

Watanabe, S.

Willemse, J.

S. M. Baumer, L. Shulepova, J. Willemse, and K. Renkmena, “Integral optical system design of injection molded optics,” Proc. SPIE 5173, 38–45 (2003).
[Crossref]

Wu, C.-C.

C.-W. Liu, C.-C. Wu, and S.-C. Lin, “A simple and wide-range refractive index measuring approach by using a sub-microngrating,” Appl. Phys. Lett. 106(15), 151907 (2015).
[Crossref]

Xu, Y.

Yin, C.

Yu, L.

Yu, Y.

S. Shin and Y. Yu, “Determining the Refractive Index and Three-Dimensional Shape of an Optical Component using Digital Holographic Microscopy with Liquid,” Korean J. Opt. Photon. 25(3), 137–141 (2014).
[Crossref]

Zheng, Y.

Appl. Opt. (7)

Appl. Phys. Lett. (2)

I. Bányász, “Direct measurement of the refractive index profile of phase gratings, recorded in silver halide holographic materials by phase-contrast microscopy,” Appl. Phys. Lett. 83(21), 4282–4284 (2003).
[Crossref]

C.-W. Liu, C.-C. Wu, and S.-C. Lin, “A simple and wide-range refractive index measuring approach by using a sub-microngrating,” Appl. Phys. Lett. 106(15), 151907 (2015).
[Crossref]

Instrum. Exp. Tech. (1)

G. S. Sarkisov, “Shearing interferometer with an air wedge for electron density diagnostics in a dense plasma,” Instrum. Exp. Tech. 39, 727–731 (1996).

J. Eur. Opt. Soc. (1)

M. Agour, P. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using slm-based phase retrieval and a phase diffuser,” J. Eur. Opt. Soc. 7, 12046 (2012).
[Crossref]

Korean J. Opt. Photon. (1)

S. Shin and Y. Yu, “Determining the Refractive Index and Three-Dimensional Shape of an Optical Component using Digital Holographic Microscopy with Liquid,” Korean J. Opt. Photon. 25(3), 137–141 (2014).
[Crossref]

Nanoscale Res. Lett. (1)

K.-B. Seo, B.-M. Kim, and E.-S. Kim, “Digital holographic microscopy based on a modified lateral shearing interferometer for three-dimensional visual inspection of nanoscale defects on transparent objects,” Nanoscale Res. Lett. 9(1), 471 (2014).
[Crossref] [PubMed]

Opt. Commun. (1)

S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, “Reflective grating interferometer for measuring the refractive index of transparent materials,” Opt. Commun. 118(5-6), 491–494 (1995).
[Crossref]

Opt. Eng. (3)

M. F. M. Costa, “Surface inspection by an optical triangulation method,” Opt. Eng. 35(9), 2743–2747 (1996).
[Crossref]

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54(5), 054105 (2015).
[Crossref]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (2)

T. A. Clarke, K. T. V. Grattan, and N. E. Lindsey, “Laser-based triangulation techniques in optical inspection of industrial structures,” Proc. SPIE 1332, 474–486 (1991).
[Crossref]

S. M. Baumer, L. Shulepova, J. Willemse, and K. Renkmena, “Integral optical system design of injection molded optics,” Proc. SPIE 5173, 38–45 (2003).
[Crossref]

Other (6)

http://www.etnews.com/20140314000130

http://blog.lginnotek.com/351

S. Bäumer, ed., Handbook of Plastic Optics (Wiley-VCH, 2011).

https://www.thorlabs.de/thorProduct.cfm?partnumber=352140-A&pn=352140-A

http://www.edmundoptics.com/optics/optical-lenses/ball-condenser-lenses/n-bk7-half-ball-lenses/49567/

http://www.schott.com/advanced_optics/english/download/schott-optical-glass-pocket-catalog-january-2014-row.pdf

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Figures (17)

Fig. 1
Fig. 1 Formation of the holographic interference pattern in the MLSI system based on a concept of the sub-divided two beam interference (STBI)
Fig. 2
Fig. 2 Optical configuration of the proposed SA-OHI system
Fig. 3
Fig. 3 Operational principle of the proposed system
Fig. 4
Fig. 4 LSD variations depending on the IA and thickness of the window glass in the (a) proposed and (b) conventional systems, respectively
Fig. 5
Fig. 5 Schematic diagrams of the allowable locations of the target object in the (a) conventional and (b) proposed systems
Fig. 6
Fig. 6 EIAs between two half-object and half-reference beams and its dependence on the location and size of the target object
Fig. 7
Fig. 7 EIA dependence on the LSD in the proposed system
Fig. 8
Fig. 8 Maximum measurable object size depending on the LSD in the proposed system
Fig. 9
Fig. 9 Maximum measurable object size depending on the EIA in the proposed system
Fig. 10
Fig. 10 Occurrence of the duplicate image problem depending on the relationship between the LSD, and the size and location of the target object
Fig. 11
Fig. 11 Overall block-diagram of the proposed system composed of three processes such as optical detection, digital reconstruction of the hologram patterns, and extraction of 3-D shape and refractive-index profiles
Fig. 12
Fig. 12 Optical experimental setup of the proposed system
Fig. 13
Fig. 13 Captured object and reference hologram patterns (a), (e) and (c), (g) from the conventional system for the case of the aspheric and half ball lenses, and (b), (f) and (d), (h) from the proposed systems for the case of the aspheric and half ball lenses, respectively
Fig. 14
Fig. 14 Block-diagram of the digital reconstruction process of the captured hologram patterns for extraction of 3-D shapes and refractive-index profiles
Fig. 15
Fig. 15 Phase information of the aspheric and half ball lenses extracted from the captured hologram patterns in the (a), (c) Conventional and (b), (d) Proposed systems
Fig. 16
Fig. 16 3-D surface profiles of the aspheric and half ball lenses calculated from their phase data of Figs. 15(a)-15(d), respectively
Fig. 17
Fig. 17 Differences between the designed and measured refractive-index distributions of the aspheric lens in the (a) 1-D, (b) 2-D and (c) 3-D forms, as well as those of the half ball lens in the (d) 1-D, (e) 2-D and (f) 3-D forms, respectively

Tables (1)

Tables Icon

Table 1 Comparison results of the key parameters between the conventional and proposed systems

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

d=2tcos θ i tan( sin 1 ( n 1 n 2 sin θ i ) )
θ t =arccos( d 2r )
S EIA =4π r 2 θ t rdsin θ t
l= t 1 d ' tan( θ 1 θ 2 )
θ 1 θ 2 =arctan( t 1 d ' l )
θ t =arccos( d ' 2r )=arccos( dcos( θ 1 θ 2 ) 2r )
S EIA =4π r 2 θ t r d ' sin θ t =4π r 2 θ t rdcos( θ 1 θ 2 )sin θ t
I(x,y)= | O 1 (x,y)+ R 2 (x,y) | 2 = | O 1 | 2 + | R 2 | 2 + O 1 * R 2 + O 1 R 2 *
U(x,y,0)= O 1 (x,y) R 2 (x,y)
U ^ ( f x , f y ,0)= U(x,y,0)exp{ j2π( f x x+ f y y) }dxdy
U ^ L ( f x , f y ,0)= n=1 L m=1 L δ( f x f x n , f y f y m ,0) U ^ ( f x , f y ,0)
U ^ L ( f x , f y ,z)= U ^ L ( f x , f y ,0)exp{ ik 1 λ 2 f x 2 λ 2 f y 2 z }
U(x,y,z)= U ^ L ( f x , f y ,z)exp{ j2π( f x x+ f y y) }d f x d f y
I(x,y,z)= | U(x,y,z) | 2
ϕ(x,y,z)=arctan{ Im[U(x,y,z] Re[U(x,y,z] }
ϕ O (x,y,d)=arctan{ Im[ U O (x,y,z] Re[ U O (x,y,z] }
ϕ R (x,y,d)=arctan{ Im[ U R (x,y,z] Re[ U R (x,y,z] }
Δϕ(x,y,z)= ϕ O (x,y,z) ϕ R (x,y,z)
Δϕ(x,y,z)= 2π λ Δn(x,y,z)ΔL(x,y,z)
ΔL(x,y,z)= n=1 O m=1 P λ 2π Δϕ(x,y,z) Δn(x,y,z)
Δn= n obj n oil
n obj = n design_obj ± σ error_obj
σ error_obj = n=1 O m=1 P λ 2π Δϕ(x,y,d) ΔL(x,y,d) ( n design_obj n oil )

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