## Abstract

In this paper, it is shown that a white light supercontinuum source generated in an air-silica microstructured optical fiber pumped with picosecond pulses offers the possibility to improve fringes visibility in interferometric acquisitions. Consequently, this source combined with a spectral interferometer, reaches high-resolution profilometric measurements. Phase calculation based on seven point algorithm can perform theoretically a subnanometer resolution. This method provides a one line profile of large surfaces from the analysis of a single shot image, without any mechanical scanning.

© 2006 Optical Society of America

## 1. Introduction

Interferometric methods are well known to achieve high resolution 3D profilometric measurements. These techniques mainly differ from each other according to the kind of light source coupled to the interferometer, and the way to analyse the interference patterns.

Phase Shifting Interferometry (PSI) techniques [1] perform 3D profilometric measurements with subnanometer resolution by analysing a few sequence of phase shifted monochromatic interferograms, but PSI fails for rough or discontinuous surfaces, because of phase ambiguity problem. Scanning White-Light Interferometry (SWLI) [2–5] overcomes this limitation, but this technique is still based on the scanning of the interferometer reference arm to restore the height surface measurement. Several articles [2–8] show that white-light interference patterns can be treated by two ways in order to get the height information of a sample : the first one consists in analysing the maximum fringe visibility [6–9]. This technique named Time-Domain Optical Coherence Tomography (TD-OCT) is commonly used to study biological sample z-depth [10]. The second way processes interferograms by phase calculation algorithms [2–5] and a resolution better than 1nm is provided. However, SWLI suffers from the time-consumed scanning procedure to record an important amount of interferograms and can decrease the signal-to-noise ratio (SNR).

In order to suppress the mechanical scanning procedure, spectroscopic measurement of white light interference patterns is realized. A fringe analysis is, by this way, achieved from a single shot image. Several techniques, based on spectral interferometry, are applied either to 3D profilometric measurements (Spectroscopic Analysis of White Light Interferograms or SAWLI [11–14]) or to biological sample tomography (Fourier-Domain Optical Coherence Tomography or FD-OCT [15–17]). SAWLI only provides a line-field imaging because the spectroscope set at the output of the interferometer uses one direction of the 2D sensor as the wavelength axis. The 2D instantaneous interference pattern obtained by SAWLI is a channelled spectrum that is processed to reconstruct one line profile of the sample. This method provides a 1nm resolution by phase analysis calculation [13]. Because the channelled spectrum is recorded from a single shot interferogram, the height measurement is kept free from the environmental noise. Then, a lateral scanning of the sample surface achieves a 3D shape measurement.

Generally, a tungsten halogen lamp, which exhibits a broadband continuous spectrum, is used for SAWLI [12–13]. This kind of sources suffers from a low power density, which limits white light interferometry to small sample areas. When larger surfaces have to be inspected, the spatial extension of the source is increased leading to the low spatial coherence reducing then fringe visibility. Super luminescent diodes (SLD) are used for surface profilometry and FD-OCT [14–15]. Contrary to halogen lamp, SLD offers a high power density which allows to analyse larger surfaces. Nevertheless, the higher temporal coherence of SLD limits spectral resolution, and contributes to a loss in channelled spectrum visibility.

In this paper, we demonstrate that spectral fringes visibility in SAWLI is improved by using a compact and efficient supercontinuum source pumped by picosecond pulses and generated in a singlemode air-silica microstructured fiber. This broadband supercontinuum source is presented by Champert and al [19]. The efficiency of sources using a broadband continuum generation in a microstructured optical fiber or crystal fiber has been proved in several domains as TD-OCT [20], projected fringe profilometry [21], but these results are performed with femtosecond laser pump leading to an expensive and complex source. The aim of this paper is to demonstrate that the association of a white light supercontinuum generated by a picosecond pump laser with a spectral interferometer provides a real improvement for high-resolution profilometry of large surface thanks to a higher source power density and a better fringe visibility.

## 2. Experimental set-up

Champert et al. [19] have proved that a flat and homogeneous continuum source in the visible range can be obtained. This continuum is performed by using a passively Q-switch Nd:YAG laser delivering 600ps pulses at λ = 1064 nm. The free space radiation of the laser is frequency doubled in a type-II KTP crystal at λ = 532 nm . These IR and green radiations are coupled into a 2 m long Microstructured Optical Fiber (MOF). At the fiber output, the broadband supercontinuum exhibits a continuous, flat and homogeneous spectral intensity distribution *B*(σ) in the visible range ∆σ, except for the wavenumber σ_{0} corresponding to an intensity peak at the doubled frequency of the laser pump (Fig. 1). Moreover, this source presents another noteworthy quality: its high power spectral density due to the photon concentration in a single mode inducing a high spatial coherence.

This source is associated to a spectral interferometer based on a Michelson interferometer, according to the experimental set-up shown in Fig. 2. After crossing the vertical slit, the white light supercontinuum is collimated by two cylindrical lenses L_{1} (f_{1}=60mm) and L_{2} (f_{2}=200mm), at the input of the interferometer. Consequently the sample under test is analysed along a vertical line. After the beam-splitter, one beam strikes the reference mirror and the other one the inspected sample. The resulting beam issued from the two interferometer arms travels through a filtering and imaging system, a spectroscope constituted of a 600 grooves/mm grating and is focused by means of a cylindrical lens L_{5} (f_{5}=50mm) on a CCD camera of 484×782 pixels. A 2D channelled spectrum is then observed along a single direction y of the sample surface by the use of the spectroscope.

As a result, the y-axis of the 2D interference pattern gives a vertical line image of the probed sample, and the x-axis corresponds to a spectral information on each wavenumber σ of the analysed bandwidth, ∆σ.

## 3. Fringe visibility study

Considering the experimental set-up, the light intensity distribution *I*(*y,σ*) , in the CCD camera plane is explained as a function of the wavenumber σ and of the optical delay τ(*y*) between the two beams by the following equation:

where: *I*
_{0} (*y*, σ) = *I*
_{1}(*y*,σ) +*I*
_{2} (*y*, σ) is the background intensity,

*I*
_{1} (*y*, σ) *and*
*I*
_{2} (*y*, σ) are the intensities in each arm,

*V*(*y*,σ) is the fringe visibility function,

and ∆Φ_{12}(τ(*y*),σ) is the phase difference between the two beams expressed by formula (2):

*c* is the light speed in the vacuum.

The interference pattern visibility depends on the spatial and temporal coherence of the light source. With a broadband light source, channelled spectrum visibility is only limited by the grating size which dictates spectrometer resolution. This condition is well realized with the light supercontinuum source and is also verified with a thermal light source (halogen lamps).

The main advantage of the light supercontinuum, obtained in a microstructured optical fiber, is the spatial coherence which induces high power density due to photon concentration in a single mode.

The fringe visibility function is compared for two filtered interferograms (Fig. 3) achieved with an halogen lamp and the broadband supercontinuum source. With the supercontinuum source (Fig. 3(a)), the intensity peak at the double frequency of the laser pump (Fig. 1) is suppressed in the frequency space by a numerical filtering of the Fourier transformed interferogram. The interference patterns are generated by introducing an optical path delay issued from two flat λ/20 mirrors.

A normalization of *V*(*y*,σ), by division of the background intensity, is processed in Fig.4 for the halogen lamp and for the white light supercontinuum. The background intensity is detected by the CCD camera when the optical delay between the two waves is highly greater than the coherence time of the source.

Figure 4 shows that the maximum fringes visibility function reaches 0.6 for the supercontinuum source whereas, for the tungsten halogen source, the visibility function does not exceed 0.3. It highly depends on the spatial coherence of the source.

## 4. Interferogram treatment and phase profile reconstruction

The previous section shows the advantage for interferometric measurements with the broadband supercontinuum source in term of fringe visibility improvement. The spectral interferograms recorded are treated, then the phase calculation is achieved by a seven point algorithm [8].

Equation 2 shows that the phase difference between the two beams of the Michelson interferometer varies linearly with the optical delay τ and consequently with the optical path difference. This optical path difference is connected to the sample height profile *z* . Therefore, z can be determined by a slope calculation of the phase as a function of the wavenumber (Eq. 3).

The phase profile reconstruction is separated in four steps:

- median filtering operation,
- phase calculation by a seven point algorithm,
- sample height profile z reconstruction by slope calculation,
- readjustment to absolute height profile z.

First of all, to efficiently achieve phase analysis by a seven point algorithm, the interferometer must be sufficiently unbalanced, in order to separate inter-correlation and autocorrelation peaks in the Fourier space.

The phase is performed by a seven point algorithm phase calculation [8]. This technique consists in extracting, along the same interferogram line, several π/2 shifted intensities *I*
_{1 to 7}. The phase shift π/2 must be expressed as a function of the wavenumber axis. The wavenumber shift δσ corresponding to a σ/2 phase shift is given by the following expression:

where *n* is the inter-correlation pixel peak position in the Fourier space, ∆σ is the analysed bandwidth.

The phase is then calculated modulo 2π using Eq. 5:

This algorithm is applied in parallel for each wavenumber of each interferogram line. From every analysed line, the wrapped phase signal is calculated with a high resolution. The unwrapped phase signal is then easily calculated independently on each line.

The next step of this analysis consists in determining the slope of the phase along the chromatic axis for each interferogram line and in converting it into a variation of height profile *z* along the vertical line, thanks to Eq. 3. Finally, the absolute height profile is determined [8]. The resolution of this technique is calculated by mean of a mathematical model, and can be less than 1nm, in the case of a highly signal to noise ratio interferogram.

The validity of this algorithm, is now tested onto a simulated interferogram (see Fig. 5) corresponding to a profile with a sharp discontinuity. In Fig. 6, the profile model and the estimated one with the seven point algorithm are represented.

The maximum error between the model and its seven point algorithm’s estimation is 0.2nm, even for the non continuous part of the profile (Fig. 7). The restitution of the profile by this algorithm does not depend on the neighboring line, consequently the only limitation of this method comes from the optical system and from fringes visibility.

## 5. Experimental results

A median filtered interferogram obtained with a plane mirror with surface flatness of λ/20 , is represented in Fig. 8. A significant decrease of the laser pump peak intensity in the recorded interferogram is achieved by division of the background intensity. A one line profile is then calculated according to the algorithms presented in the previous section. This profile is shown in Fig. 9.

The maximum deviation is 6nm. The accuracy of the mirror surface flatness is then equivalent to the one given by the constructor. Due to imaging system used, the measured spatial resolution along the y axis is 40μm, and the observed line length is 19mm.

The same process applied to another mirror which defaults are higher than λ/2, is achieved. In the Figs. 10 and 11, the resulting treated interferogram and the corresponding reconstructed profile are respectively represented.

The one line profile of this mirror is well performed by an absolute phase calculation based on the seven point algorithm. We finally obtain a 60nm maximum deviation on this profile. The spatial resolution along the y axis is measured to be 18μm, and the observed line length is 2.5mm. However, we can notice that due to the poor quality of the mirror, no interference patterns can even be recorded with a halogen lamp.

It is possible to perform high resolution profilometric measurements with this technique, on sample which surface flatness is highly better than lambda (Fig. 9). In the case of the low quality mirror, the supercontinuum source provides interference patterns with improved visibility yielding possible the reconstruction of a one line profile with a signal to noise ratio increased (Fig. 11).

## 6. Conclusion

We presented a well known procedure to achieve a one line profile of a large surface, based on a multispectral interferometric measurement and a seven point algorithm phase calculation. The originality of this work consists in the use of a white light supercontinuum source which improves the fringes visibility of the recorded interferograms. Thus, high resolution profilometric measurements on large surfaces become possible. Moreover, a lateral scanning of the sample surface has to be performed with a stepping motor or a galvanometer mirror in order to achieve a complete 3D shape measurement [14].

The robustness of the seven point algorithm from a simulated profile is demonstrated. This algorithm provides a subnanometer resolution for highly contrasted interferograms. As a result, the association of white light supercontinuum source with a spectral interferometer provides a real improvement for profilometric measurements. We demonstrated that this super continuum source is of interest for profilometry and we are also employing it for others applications as the characterization of graded index optical component by spectral interferometry and the z-depth measurement of biological sample by FD-OCT. This works will be exposed in further publications.

A new generation of white light supercontinuum source is developed at the *Institut de Recherche en Communication Optiques et Microondes* (IRCOM) [22], with no peak intensity in the spectral intensity distribution *B*(σ). This new source is of great interest for our works.

## Acknowledgments

We thank Vincent Coudert and his team from *Institut de Recherche en Communication Optiques et Microondes* (IRCOM) for this beneficial collaboration.

## References and links

**01. **K. Creath, “Phase Measurement Interferometry Techniques,” in Progress in Optics, Vol. XXVI, E. Wolf, Ed. Elsevier Science Publishers, Amsterdam, pp. 349–393(1988).

**02. **P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. **32**, 3438–3441 (1993) [CrossRef] [PubMed]

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

**04. **P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. of Mod. Opt. **42**.2, 389–401 (1995). [CrossRef]

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

**06. **T. Dresel, G. Haüsler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. **31**, 919–925 (1992). [CrossRef] [PubMed]

**07. **K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A **13**, 832–843 (1996). [CrossRef]

**08. **P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white light phase-shifting interferometry,” J. of Mod. Opt. **44**, 519–534 (1997) [CrossRef]

**09. **P. de Groot, X. Colonna de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. **41**, 4571–4578 (2002). [CrossRef] [PubMed]

**10. **D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto. Optical coherence tomography. Science **254**, 1178–1181 (1991).

**11. **J. Schwider and L. Zhou, “Dispersive interferometric profilometer,” Opt. Lett. **19**, 995–997 (1994) [CrossRef] [PubMed]

**12. **J. E. Calatroni, P. Sandoz, and Gilbert Tribillon, “Surface profiling by means of double spectral modulation,” Appl. Opt. **32**, 30–36 (1993) [CrossRef] [PubMed]

**13. **P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using calculation algorithms for spectroscopic analysis of white-light interferograms,” J. of Mod. Opt. **43**, 701–708 (1996). [CrossRef]

**14. **T. Endo, Y. Yasuno, S. Makita, M. Itoh, and T. Yatagai, “Profilometry with line-field Fourier-domain interferometry,” Opt. Express **13**, 695–701 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-695 [CrossRef] [PubMed]

**15. **B. Grajciar, M. Pircher, A. F. Fercher, and R. A. Leitgeb, “Parallel Fourier domain optical coherence tomography for in vivo measurement of the human eye,” Opt. Express **13**, 1131–1137 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1131 [CrossRef] [PubMed]

**16. **A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, “Measurement of Intraocular Distances by Backscattering Spectral Interferometry,” Opt. Commun. **117**, 43–48 (1995). [CrossRef]

**17. **M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. **27**, 1415–1417 (2002). [CrossRef]

**18. **B. Grajciar, M. Pircher, A. F. Fercher, and R. A. Leitgeb, “Parallel Fourier domain optical coherence tomography for in vivo measurement of the human eye,” Opt. Express **13**, 1131–1137 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1131 [CrossRef] [PubMed]

**19. **P. Champert, V. Couderc, P. Leproux, S. Février, V. Tombelaine, L. Labonté, P. Roy, C. Froehly, and P. Nérin, “White-light supercontinuum generation in normally dispersive optical fiber using original multi-wavelength pumping system,” Opt. Express **12**, 4366–4371 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4366 [CrossRef] [PubMed]

**20. **Y. Wang, Y. Zhao, J. Nelson, Z. Chen, and R. Windeler, “Ultrahigh-resolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber,” Opt. Lett. **28**, 182–184 (2003) [CrossRef] [PubMed]

**21. **W. Su, K. Shi, Z. Liu, B. Wang, K. Reichard, and S. Yin, “A large-depth-of-field projected fringe profilometry using supercontinuum light illumination,” Opt. Express **13**, 1025–1032 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-1025 [CrossRef] [PubMed]

**22. **V. Tombelaine, C. Lesvigne, P. Leproux, L. Grossard, V. Couderc, J. Auguste, J. Blondy, G. Huss, and P. Pioger, “Ultra wide band supercontinuum generation in air-silica holey fibers by SHG-induced modulation instabilities,” Opt. Express **13**, 7399–7404 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7399 [CrossRef] [PubMed]