Abstract

We describe a single-shot technique to measure areal profiles on optically smooth and stepped surfaces for applications where rapid data acquisition in non-cooperative environments is essential. It is based on hyperspectral interferometry (HSI), a technique in which the output of a white-light interferometer provides the input to a hyperspectral imaging system. Previous HSI implementations suffered from inefficient utilisation of the available pixels which limited the number of measured coordinates and/or unambiguous depth range. In the current paper a >20-fold increase in pixel utilisation is achieved through the use of a 2-D microlens array, that leads to a 35 × 35 channel system with an unambiguous depth range of 0.88 mm.

© 2017 Optical Society of America

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References

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2012 (1)

2010 (1)

J. M. Huntley, T. Widjanarko, and P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010).

1997 (1)

1995 (1)

R. Bacon and et al.., “3d spectrography at high spatial resolution. I. Concept and realization of the integral field spectrograph tiger,” Astron. Astrophys. Suppl. Ser. 113, 347–357 (1995).

1994 (2)

1993 (1)

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).

1992 (1)

1986 (1)

J. M. Huntley, “An image processing system for the analysis of speckle photographs,” J. Phys. E Sci. Instrum. 19, 43–49 (1986).

Bacon, R.

R. Bacon and et al.., “3d spectrography at high spatial resolution. I. Concept and realization of the integral field spectrograph tiger,” Astron. Astrophys. Suppl. Ser. 113, 347–357 (1995).

de Groot, P.

Deck, L.

Dresel, T.

Häusler, G.

Huntley, J. M.

T. Widjanarko, J. M. Huntley, and P. D. Ruiz, “Single-shot profilometry of rough surfaces using hyperspectral interferometry,” Opt. Lett. 37(3), 350–352 (2012).
[PubMed]

J. M. Huntley, T. Widjanarko, and P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010).

J. M. Huntley, “An image processing system for the analysis of speckle photographs,” J. Phys. E Sci. Instrum. 19, 43–49 (1986).

Kuwamura, S.

Ruiz, P. D.

T. Widjanarko, J. M. Huntley, and P. D. Ruiz, “Single-shot profilometry of rough surfaces using hyperspectral interferometry,” Opt. Lett. 37(3), 350–352 (2012).
[PubMed]

J. M. Huntley, T. Widjanarko, and P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010).

Sandoz, P.

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).

Takeda, M.

Tribillon, G.

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).

Venzke, H.

Widjanarko, T.

T. Widjanarko, J. M. Huntley, and P. D. Ruiz, “Single-shot profilometry of rough surfaces using hyperspectral interferometry,” Opt. Lett. 37(3), 350–352 (2012).
[PubMed]

J. M. Huntley, T. Widjanarko, and P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010).

Yamaguchi, I.

Yamamoto, H.

Appl. Opt. (4)

Astron. Astrophys. Suppl. Ser. (1)

R. Bacon and et al.., “3d spectrography at high spatial resolution. I. Concept and realization of the integral field spectrograph tiger,” Astron. Astrophys. Suppl. Ser. 113, 347–357 (1995).

J. Mod. Opt. (1)

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).

J. Phys. E Sci. Instrum. (1)

J. M. Huntley, “An image processing system for the analysis of speckle photographs,” J. Phys. E Sci. Instrum. 19, 43–49 (1986).

Meas. Sci. Technol. (1)

J. M. Huntley, T. Widjanarko, and P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010).

Opt. Lett. (1)

Other (1)

M. Shepherd, “Correct sampling of diffraction limited images,” (California Institute of Technology, CCAT-p, 2012). Technical Memo. http:// wiki.astro.cornell.edu/twiki/pub/CCAT/CCAT_Memos/DiffractionLimitedSampling111212.pdf

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Figures (9)

Fig. 1
Fig. 1

Optical setup of the Hyperspectral Interferometry system based on a microlens array, showing: SLD: Super-luminescent light emitting diode; FBG1, FBG2: Fibre Bragg gratings; Lc: collimator; BS: beam splitter; O: object; R: reference mirror; L0, L1, L2, L4 and L5: NIR achromatic lenses; E1: aperture stop; MLA: microlens array; L3: lenslet; G: diffraction grating and PDA: photodetector array. At the top of the imaging interferometer box, the ‘two wavelengths’ and ‘broadband’ illumination configurations are shown.

Fig. 2
Fig. 2

Encoding of surface height in Hyperspectral Interferometry: a) object with a surface step profile. The insert above shows a cross-section through the sample with height distribution h(x, y). Lines indicating cross-sections through the zero optical path difference and sample datum surfaces are also shown; b) image of the object on the microlens array; c) microlens array pupils’ plane; d) array of spectra (no reference beam in the interferometer); e) spectra (shown here in monochrome for clarity) are modulated by fringes which frequency encode surface height from datum.

Fig. 3
Fig. 3

Close-up of the spectra corresponding to the focal spots of the microlens array in the ‘two wavelengths’ configuration. The two crosses indicate the position of the λ1 and λ2 peaks from a single pupil, which are separated by a distance d on the PDA.

Fig. 4
Fig. 4

Spatial distribution of the distance d between the λ1 and λ2 peak locations in the spectra.

Fig. 5
Fig. 5

Close-up of the 1-D horizontal interference patterns produced by dispersion of the focal spots of the microlens array when ‘broadband’ illumination is used. The dc term of the interference signal has been removed, so mid grey represents zero while darker and brighter levels represent negative and positive values, respectively.

Fig. 6
Fig. 6

Spectral interference profile for one lenslet after removal of the dc component: a) intensity signal; b) Fourier Transform of (a) (output of Fast Fourier Transform algorithm shown as open circles, with the continuous Fourier transform overlaid as a continuous line), from which the peak position (vertical line) is evaluated; c) as (b) but after scaling frequency to distance.

Fig. 7
Fig. 7

Three surface height measurements of a flat mirror with normal shifts of 50 μm.

Fig. 8
Fig. 8

(a) Residual of the height map h(x, y) shown at the top in Fig. (7) with respect to a linear fit (in μm). (b) and (c) show, respectively, the spatial variation of the horizontal and vertical extent (measured in pixels) of the spots corresponding to λ2 imaged at the PDA when the reference arm is blocked. These correspond to the standard deviations of a 2D-Gaussian best fit in the horizontal and vertical directions.

Fig. 9
Fig. 9

Surface profile of the edge of a circular microscope cover slip on a glass substrate measured using 35 × 35 lenslets of the MLA.

Equations (17)

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0z z M ,
z M = π δk ,
δz=γ 2π N k δk ,
z=2[ h 0 h(x,y) ],
m 21 = f 2 / f 1 ,
NA 2 λ c 4 p x MLA ,
D 1 =2 f 2 NA 2 .
d PSF3 =1.22 λ c / NA 3 .
d PSF5 4.88 p x PDA ,
m 54 min =4.88 p x PDA / d PSF3 .
N x PDA =4.88 L x MLA / d PSF3 ,
R= p x MLA / d PSF3 ,
l s PDA = p x MLA m 54 (R+1),
sin β d =λFsin β i ,
β i = tan 1 ( x MLA f 4 ),
x m,n PDA (λ)= f 5 tan{ sin 1 [ λFsin β i ] sin 1 [ λ 1 Fsin β i ] }.
z= f k 2π Δk ,