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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 27 — Dec. 17, 2012
  • pp: 28631–28640
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Topographic optical profilometry by absorption in liquids

Juan Carlos Martinez Antón, Jose Alonso, Jose Antonio Gómez Pedrero, and Juan Antonio Quiroga  »View Author Affiliations


Optics Express, Vol. 20, Issue 27, pp. 28631-28640 (2012)
http://dx.doi.org/10.1364/OE.20.028631


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Abstract

Optical absorbance within a liquid is used as a photometric probe to measure the topography of optical surfaces relative to a reference. The liquid fills the gap between the reference surface and the measuring surface. By comparing two transmission images at different wavelengths we can profile the height distribution in a simple and reliable way. The presented method handles steep surface slopes (<90°) without difficulty. It adapts well to any field of view and height range (peak to valley). A height resolution in the order of the nanometer may be achieved and the height range can be tailored by adapting the concentration of water soluble dyes. It is especially appropriate for 3D profiling of transparent complex optical surfaces, like those found in micro-optic arrays and for Fresnel, aspheric or free-form lenses, which are very difficult to measure by other optical methods. We show some experimental results to validate its capabilities as a metrological tool and handling of steep surface slopes.

© 2012 OSA

1. Introduction

Profilometry of optical surfaces is of increasing importance and difficulty as optical devices expand its applications and surface topologies are more complex, like in Fresnel optics, micro-optical arrays, free-form lenses [1

1. K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News 23(6), 30–35 (2012). [CrossRef]

], etc… There are numerous non-contact optical methods to determine the topography of surfaces. Most of them use the reflection of light on the surface to be measured and they are mainly based on interferometry [2

2. C. C. Lai and I. J. Hsu, “Surface profilometry with composite interferometer,” Opt. Express 15(21), 13949–13956 (2007). [CrossRef] [PubMed]

4

4. J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE 6024, 602401, 602401-11 (2006). [CrossRef]

], confocal profilometry [5

5. C. Zhao, J. Tan, J. Tang, T. Liu, and J. Liu, “Confocal simultaneous phase-shifting interferometry,” Appl. Opt. 50(5), 655–661 (2011). [CrossRef] [PubMed]

,6

6. C. H. Lee, H. Y. Mong, and W. C. Lin, “Noninterferometric wide-field optical profilometry with nanometer depth resolution,” Opt. Lett. 27(20), 1773–1775 (2002). [CrossRef] [PubMed]

] and structured light projection and triangulation techniques [7

7. F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13(1), 231–243 (2004). [CrossRef]

,8

8. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000). [CrossRef]

]. However, for most conventional approaches, a high surface slope is difficult to handle. Different aspects are behind this fact, being the more basic that the light is lost when reflection occurs at high surface slopes.

In this work, we propose an optical profilometric method that works with transmitted light and is based on the optical absorption in a dye solution, which codifies height variations. The use of transmitted light through liquids is interesting for the optical determination of surface topography [9

9. D. Purcell, A. Suratkar, A. Davies, F. Farahi, H. Ottevaere, and H. Thienpont, “Interferometric technique for faceted microstructure metrology using an index matching liquid,” Appl. Opt. 49(4), 732–738 (2010). [CrossRef] [PubMed]

15

15. M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc. 231(1), 156–167 (2008). [CrossRef] [PubMed]

]. In the work of Purcell et al [9

9. D. Purcell, A. Suratkar, A. Davies, F. Farahi, H. Ottevaere, and H. Thienpont, “Interferometric technique for faceted microstructure metrology using an index matching liquid,” Appl. Opt. 49(4), 732–738 (2010). [CrossRef] [PubMed]

] a non-absorbing liquid is used to reduce the apparent surface slope by index matching with the surface materials and therefore controlling refraction. This allows the use of known interference techniques to explore micro-prisms and other steep surface profiles successfully [9

9. D. Purcell, A. Suratkar, A. Davies, F. Farahi, H. Ottevaere, and H. Thienpont, “Interferometric technique for faceted microstructure metrology using an index matching liquid,” Appl. Opt. 49(4), 732–738 (2010). [CrossRef] [PubMed]

]. On the other hand, the use of optical absorption to estimate depth or thickness is not new [10

10. G. Svensson, “A method for measurement of the absorption in extremely high-absorbing solutions,” Exp. Cell Res. 9(3), 428–433 (1955). [CrossRef] [PubMed]

15

15. M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc. 231(1), 156–167 (2008). [CrossRef] [PubMed]

]. Although the Lambert-Beer law is commonly used to calculate the specific absorption of substances [10

10. G. Svensson, “A method for measurement of the absorption in extremely high-absorbing solutions,” Exp. Cell Res. 9(3), 428–433 (1955). [CrossRef] [PubMed]

,11

11. M. Csete and Z. Bor, “Plano-concave microcuvette for measuring the absorption coefficient of highly absorbing liquids,” Appl. Opt. 36(10), 2133–2138 (1997). [CrossRef] [PubMed]

], it can be seen the other way around, i.e., used to estimate the thickness of solid films [12

12. J. Johnson and T. Harris, “Full-field optical thickness profilometry of semitransparent thin films with transmission densitometry,” Appl. Opt. 49(15), 2920–2928 (2010). [CrossRef] [PubMed]

], or more interesting to our goal, to obtain the relative profile of a surface compared to a reference surface when a liquid with known absorption fills the space between both elements [13

13. S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol. 21(1), 61–66 (2002). [CrossRef]

15

15. M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc. 231(1), 156–167 (2008). [CrossRef] [PubMed]

]. To apply this last strategy correctly a reference optical signal is necessary. In the work of Ogilvie et al [13

13. S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol. 21(1), 61–66 (2002). [CrossRef]

,14

14. E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett. 191(3-4), 267–282 (2001). [CrossRef]

] this is accomplished by using clear water instead of the dye solution in the same setup. This approach is cumbersome and the procedure is prone to misalignment and other errors like dye contamination. Model et al [15

15. M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc. 231(1), 156–167 (2008). [CrossRef] [PubMed]

] work under the assumption of constant irradiance over the surface. But in their setup, the aperture limited illumination may lead to profile errors particularly for very steep surfaces, where again, light may be lost by refraction.

We introduce two improvements in the topographic optical profilometry by absorption in fluids which lead to a greater reliability of the technique. First, we use two narrow spectral bands for illuminating. In this way, we get an absorption signal and a reference signal without moving any component in the setup. Furthermore, a constant ratio between the radiances of both spectral bands guarantees a non-distorted profile measurement. Secondly, we use extended light sources to reach high numerical apertures of illumination. This strategy allows measuring steep slopes (<90°) in a simple way.

2. Description of the method

A reference surface is located close to the surface we want to profile (Fig. 1
Fig. 1 Basic configuration for the sample to be measured.
). An optical absorbing liquid or fluid fills the gap between the surface to measure and a reference surface. This optical sandwich is situated between an extended light source and an imaging device focused at the surface to profile. Images are captured for different spectral bands. The differential absorption between these bands provides direct information of the surface topography. The basic procedure consists on taking images at two narrow spectral bands centered at λA and λR. They are selected so that the absorption of the dye is significantly greater at λA, and the band centered at λR is used to provide a reference signal.

An extended light source provides wide spread angular illumination (for example an integrating sphere). Also, a diffusing element optically coupled may also be used to increase the illuminating angular aperture at the surface to profile (Fig. 1). In this way, at every point of the surface to profile, we make sure that the light beams will reach the entrance pupil of the imaging device, independently of ray refraction at slopes.

There are several ways to measure the transmittance within the liquid which is the basis for the profilometric probe. We describe here our preferred procedure because its simplicity and robustness. The imaging system provides an image proportional to the transmitted radiance L of the sample that can be expressed as (Lambert-Beer law)
L=L0Texp(αt),
(1)
where L0 is the radiance of the extended light source taken at the considered surface point and line of sight (beam trajectory), T is the total transmittance of the measuring plate-reference plate system except for the internal liquid transmittance that is included in the exponential term, where α is the absorption coefficient of the liquid and t is the distance from a reference surface point to a sample surface point as shown in Fig. 1 (consider it positive).

The characteristic parameter tS can be seen as synthetic skin depth and basically defines the height range of the method. For the particular case of zero absorption at the reference wavelength (λR), the parameter tS represents the distance that the light at absorbing wavelength (λA) propagates within the liquid just to be attenuated to ~37% (T = 1/e). As it depends on absorption, it can be set to different values simply by varying the concentration of a soluble dye. As we see next, both the achievable height resolution and the height range are linked to tS in a fundamental way.

The photometric dynamic range of the imaging capturing device determines the height profile range (peak to valley) of the method. In practice, the height range is not much bigger than tS because of the exponential decay of transmission. For example, at a depth of 4tS the transmittance is reduced to a mere ~2%. We may increase the height range by one order of magnitude and still preserving the height resolution by using high dynamic range imaging (HDRI techniques) which is equivalent to expand the photometric range of the imaging device. Notice that both height resolution and height dynamic range are linked to the fluid parameter tS and this parameter can be adapted by means of changing the dye concentration.

3. Experimental results

As a basic absorbing fluid we used a saturated solution of methyl violet dye (CAS#8004-87-3) in a mixture of water (13.5% by weight) and glycerol (86.5%) and filtered to 0.8 μm particles. The glycerol-water mixture has proven adequate to avoid evaporation/condensation of water that would change absorption properties. The ambient at the lab were typically at T = 25 ± 2°C and at a relative humidity of 51 ± 3% measured with a Brannan type hygrometer. The absorption spectrum of the liquid and the wavelengths of illumination are shown in Fig. 2. Under these conditions the fluid is found to have a tS of 6.63 ± 0.05 μm, obtained from a method we will explain later.

The digital imaging capturing device was a CCD array of 1340x1024 pixels (model ORCA C4742-96-12G04) with a well depth of 18000 electrons and a 12 bit signal digitizer. Operation was typically made between 5% and 40% of the saturation level to be sure that a deviation from linearity of the response is below 0.1%. At 40% signal level the SNR is about 80:1. A zoom lens was used to focus images on the CCD in a quasi-telecentric mode (model NT58-240 from Edmund Optics). Spatial photo-detector response non uniformity (PNRU) was also characterized by taking images of uniform irradiance coming directly from the integrating sphere at both wavelengths λA and λR. These images are used to correct the effect of PRNU. We insert in Eq. (4) the magnitude M estimated as M = Mm/Mp where Mp is the ratio of images of direct observation of extended light source at both wavelengths Mp = RA/RR (R signal at the CCD) and Mm is the equivalent ratio but with the sample-reference setup in the optical path. A maximum signal to noise ratio SNR of ~900:1 is obtained when 128 frame averaging is performed for a single image capture.

A first test was performed to validate Eq. (4) and the experimental setup and also served to obtain the parameter tS of the prepared absorption solution. Two flats were arranged to make a very thin wedge prism, partially filled with the absorber and partially filled with air. One flat is λ/20 and the other is λ/10. Under the illumination setup described we obtain the image in Fig. 3(a)
Fig. 3 (a) Image of a thin wedge between flats and partially filled with absorbing fluid. Interference fringes are observed at the air gap. (b) Signal profile along the line drawn in (a). Notice the exponential decay in the absorption region and the fringe contrast in the air gap side. (c) Topographic image of the wedge of by processing the image of (a) applying Eq. (4). (d) Height profile along the line drawn in (c), ordinate axis is in microns.
. There we find a variable absorption area corresponding to the region of the prismatic gap filled with the liquid, and also a fringe interference pattern in the other side. In the fringed interference region we make a simple calculation of thickness slope perpendicular to the fringes. Each fringe corresponds with a λ/2 height increment ( = 266 nm). From the interference fringe analysis we obtain a wedge slope of Δtx = (2.16 ± 0.01)·10−4, which represents a height variation of 0.216 μm per millimeter of length perpendicular to the fringe pattern. In the absorbing side we can obtain the maximum slope of ln(M) which we know is proportional to the height variation. The proportionality constant is the absorption parameter tS (Eq. (4)). The comparison with the interference data get the result of tS = 6.63 ± 0.05 μm.

Applying Eq. (4) with the estimated tS we obtain the results shown in Fig. 3(d). We may appreciate a linear thickness profile as was expected from a wedge. A more exigent data processing is shown in Fig. 4
Fig. 4 Residuals of a regression fit to a plane for the image of Fig. 4. Regression is only computed within the red polygon drawn.
where we show the residuals of a regression fit to a plane for the ln(M) image. A region of interest (red polygon in the figure) was selected for the regression in order to avoid bubbles that may distort the result. We obtain a RMS form deviation of ± 22 nm and a peak to valley deviation of ~65 nm which is in agreement with the nominal data of the surfaces, a λ/10 flat on a λ/20 flat (or an equivalent peak to valley deviation of 90 nm at worst). Some diagonal nearly parallel lines are observed crossing the field of view. After cleaning and observing the sample flat under intense illumination, scattered light confirmed the presence of slight scratches that explain this feature. In the Fig. 4 we may also appreciate on the left and on top some curved strips that are probably due to residual humidity in the flat surface coming from a preliminary wet cleaning. This humidity residue changes locally the absorption of the liquid and provokes these artifacts.

A second topographic measurement was performed on a spherical surface compared against a flat surface as a reference. The sphere comes from a 1” aperture BK7 plano-convex lens (model PLCX-25.4-5151.0-C from CVI Melles Griot corp.) with a nominal radius of R = 5151 ± 26mm. The surface accuracy is stated as λ/10 (~60 nm) over the 85% of the aperture. The reference surface is a λ/20 silica flat with an aperture of 3”. The convex surface was lying down on the flat with the absorption liquid in between. Viscosity and surface tension keep the fluid in place. The other face of the flat was index matched to a diffusing opal glass and finally the stack of the three glass pieces is laid down on the exit port of the illuminating integrating sphere (~2.5” aperture).

Several measurements of the lens were performed on different days. In the mean time, the lens was rotated and displaced to extract some bubbles but keeping the same absorbing liquid and exposed to the open air. This was done to check reproducibility of measurements against evaporation/condensation and manipulation. For each measurement we take two images (at λA and λR) with background removed and correct them with PRNU images to get the processed image M. By means of Eq. (4) we obtain topographic images like the ones shown in Fig. 5
Fig. 5 Images of the synthetic transmittance M of a plano-convex lens: (a) measurement in day 1 and (b) after 5 days and rotating and displacing the lens to test reproducibility.
for day 1 and day 5. For each topographic image we make a regression fit to an ideal spherical surface. What it is shown at Fig. 6
Fig. 6 Results on the spherical surface of a spherical lens (R = 5151mm). (a) Regression fit residuals of the processed measurements of Fig. 5(a). (b) the same as (a) but for Fig. 5(b). (b) and (d) are linear profiles of fit residuals along the lines drawn in (a) and (c) respectively.
are the residuals of the regression fit for days 1 and 5. The regression is performed in a selected region (red polygon drawn in Fig. 6(a) and 6(c)) avoiding the presence of bubbles.

For the estimation of the radius of the sphere we need the length scale of the image and this was obtained from the known size of the lens (25.3 ± 0.05 mm). We also assumed no appreciable imaging distortion in the regression area. The method finally provides good results, matching the expectations. From 5 different measurements we obtain an averaged radius of curvature of R = 5170 ± 60mm which agrees with the nominal data of R = 5151 ± 26mm. Possible time-shifts or evaporation effects are included in the uncertainty but are practically unappreciable. The RMS form deviation for each regression fit is around ~ ± 27 nm which is in agreement with the nominal figure of merit for a λ/10 surface. Height resolution according to Eq. (5) is expected to be around ~ ± 15 nm, which is consistent with the observed residuals in Fig. 6(b) and 6(d). Finally, appreciable deviations of residuals are observed at the rim of the lens but these are still consistent with being a nominal λ/10 surface only over the 85% of the aperture.

Although the former tests demonstrate the capabilities of the method as a reliable metrological tool, perhaps it does not add special value to measure spheres, mild aspheres or flats, for which standard interferometric tools are well established and recognized. On the contrary, the method may stand out for measuring complicated shapes and high slopes on macro and micro optical components and arrays. For them, the method still provides speed, height resolution and accuracy with a simple and robust experimental procedure.

For example, Fig. 7
Fig. 7 Topography of a cylindrical lens array. (a) 3D rendering of a profilometric measurement. (b) Partial linear profile along a line perpendicular to the array axis.
shows the results for a cylindrical micro-lens array of 64 lenses per inch and nominal sag of 18 μm in quite agreement with extracted profile (Fig. 7(b)). In another example, we show in Fig. 8
Fig. 8 Prismatic array. (a) image ratio M, (b) partial height profile perpendicular to prism edges (c) 3D representation of the full field of view.
the measurement of a micro-prism linear array used in eye care. It has a peak to valley height of 57 μm and a period of 1.43 mm. Absorption solution in this case was diluted to have tS = 85 μm. A maximum nominal slope of 90° is expected at the edges of the prisms. In practice, we find in the measurement that the abrupt height change is handled without difficulty, although somewhat smoothed due to the lateral imaging resolution (Fig. 8). Finally, we show in Fig. 9
Fig. 9 Linear array of prisms (apex of 60°). (a) 3D rendering of processed image ratio M, (b) height profile along a line perpendicular to prism wedges. Notice the horizontal and vertical scales are the same in both representations.
the results for a measured linear array or prisms with facets symmetrically arranged at an angle of 60°, and at a period of 0.64 mm (Fresnel Technologies part#420). For this sample we use a dye solution with tS = 754 μm. The results shown in the linear profiles are in good agreement with the nominal values expected for all the arrays. Some particles contamination is noticeable in the case of the prism array of Fig. 8 and also bubbles are usually present in all measurements. They behave as blind spots but do not affect the processing of information of nearby areas because Eq. (4) is applied for every single pixel independently of the neighbors.

5. Conclusions

We demonstrate the feasibility of topographic optical profilometry by absorption in liquids. The method is especially appropriate for all type of transmission optical devices with complex surface forms and patterns. Height resolution and form accuracy in the order of the nanometer has been achieved. The method can handle steep surface slopes in contrast to other know reflection based techniques. We may point out also other features: 1) it is simple to implement with no-moving parts in contrast to confocal and/or interferometric profilometers and 2) it can be fast besides some sample preparation that is required.

Acknowledgments

This work has been developed within the framework of the project DPI2009-09023 financially supported by Spanish MICINN (Ministerio de Ciencia e Innovación).

References and links

1.

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News 23(6), 30–35 (2012). [CrossRef]

2.

C. C. Lai and I. J. Hsu, “Surface profilometry with composite interferometer,” Opt. Express 15(21), 13949–13956 (2007). [CrossRef] [PubMed]

3.

L. Deck and P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33(31), 7334–7338 (1994). [CrossRef] [PubMed]

4.

J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE 6024, 602401, 602401-11 (2006). [CrossRef]

5.

C. Zhao, J. Tan, J. Tang, T. Liu, and J. Liu, “Confocal simultaneous phase-shifting interferometry,” Appl. Opt. 50(5), 655–661 (2011). [CrossRef] [PubMed]

6.

C. H. Lee, H. Y. Mong, and W. C. Lin, “Noninterferometric wide-field optical profilometry with nanometer depth resolution,” Opt. Lett. 27(20), 1773–1775 (2002). [CrossRef] [PubMed]

7.

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13(1), 231–243 (2004). [CrossRef]

8.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000). [CrossRef]

9.

D. Purcell, A. Suratkar, A. Davies, F. Farahi, H. Ottevaere, and H. Thienpont, “Interferometric technique for faceted microstructure metrology using an index matching liquid,” Appl. Opt. 49(4), 732–738 (2010). [CrossRef] [PubMed]

10.

G. Svensson, “A method for measurement of the absorption in extremely high-absorbing solutions,” Exp. Cell Res. 9(3), 428–433 (1955). [CrossRef] [PubMed]

11.

M. Csete and Z. Bor, “Plano-concave microcuvette for measuring the absorption coefficient of highly absorbing liquids,” Appl. Opt. 36(10), 2133–2138 (1997). [CrossRef] [PubMed]

12.

J. Johnson and T. Harris, “Full-field optical thickness profilometry of semitransparent thin films with transmission densitometry,” Appl. Opt. 49(15), 2920–2928 (2010). [CrossRef] [PubMed]

13.

S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol. 21(1), 61–66 (2002). [CrossRef]

14.

E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett. 191(3-4), 267–282 (2001). [CrossRef]

15.

M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc. 231(1), 156–167 (2008). [CrossRef] [PubMed]

16.

J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE 8169, 816910-8 (2011). [CrossRef]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.1250) Optical design and fabrication : Aspherics
(230.3990) Optical devices : Micro-optical devices
(110.4155) Imaging systems : Multiframe image processing

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: September 27, 2012
Revised Manuscript: November 11, 2012
Manuscript Accepted: November 18, 2012
Published: December 10, 2012

Citation
Juan Carlos Martinez Antón, Jose Alonso, Jose Antonio Gómez Pedrero, and Juan Antonio Quiroga, "Topographic optical profilometry by absorption in liquids," Opt. Express 20, 28631-28640 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28631


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References

  1. K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News23(6), 30–35 (2012). [CrossRef]
  2. C. C. Lai and I. J. Hsu, “Surface profilometry with composite interferometer,” Opt. Express15(21), 13949–13956 (2007). [CrossRef] [PubMed]
  3. L. Deck and P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt.33(31), 7334–7338 (1994). [CrossRef] [PubMed]
  4. J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE6024, 602401, 602401-11 (2006). [CrossRef]
  5. C. Zhao, J. Tan, J. Tang, T. Liu, and J. Liu, “Confocal simultaneous phase-shifting interferometry,” Appl. Opt.50(5), 655–661 (2011). [CrossRef] [PubMed]
  6. C. H. Lee, H. Y. Mong, and W. C. Lin, “Noninterferometric wide-field optical profilometry with nanometer depth resolution,” Opt. Lett.27(20), 1773–1775 (2002). [CrossRef] [PubMed]
  7. F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–243 (2004). [CrossRef]
  8. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000). [CrossRef]
  9. D. Purcell, A. Suratkar, A. Davies, F. Farahi, H. Ottevaere, and H. Thienpont, “Interferometric technique for faceted microstructure metrology using an index matching liquid,” Appl. Opt.49(4), 732–738 (2010). [CrossRef] [PubMed]
  10. G. Svensson, “A method for measurement of the absorption in extremely high-absorbing solutions,” Exp. Cell Res.9(3), 428–433 (1955). [CrossRef] [PubMed]
  11. M. Csete and Z. Bor, “Plano-concave microcuvette for measuring the absorption coefficient of highly absorbing liquids,” Appl. Opt.36(10), 2133–2138 (1997). [CrossRef] [PubMed]
  12. J. Johnson and T. Harris, “Full-field optical thickness profilometry of semitransparent thin films with transmission densitometry,” Appl. Opt.49(15), 2920–2928 (2010). [CrossRef] [PubMed]
  13. S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol.21(1), 61–66 (2002). [CrossRef]
  14. E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett.191(3-4), 267–282 (2001). [CrossRef]
  15. M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc.231(1), 156–167 (2008). [CrossRef] [PubMed]
  16. J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE8169, 816910-8 (2011). [CrossRef]

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