Red-Green-Blue wavelength interferometry and TV holography for surface metrology

Transcription

1 J Opt (October-December 2011) 40(4): DOI /s z RESEARCH ARTICLE Red-Green-Blue wavelength interferometry and TV holography for surface metrology U. Paul Kumar & N. Krishna Mohan & M. P. Kothiyal Received: 18 April 2011 / Accepted: 31 October 2011 / Published online: 6 December 2011 # Optical Society of India 2011 Abstract Surface discontinuities greater than half a wavelength can not be measured unambiguously using single wavelength interferometry. In TV holography, it is difficult to quantify the data under relatively large loading conditions due to the overcrowding of fringes with a single wavelength. Further, single wavelength does not reveal the contour of rough surfaces with TV holography. Multiple wavelengths measurements using red, green, and blue wavelengths can overcome these problems. In this paper a multiple wavelength interferometric system with colour CCD is demonstrated for such measurements. The interference patterns are recorded by a single chip colour CCD camera which makes the data acquisition as simple as in single wavelength case. The interference pattern is decomposed into its R G B components to evaluate the phase at individual wavelengths. An eight step phase shifting algorithm is used to simplify the application of phase shifting technique in the multiple wavelength system. Experimental results on an etched silicon sample for the measurement of large discontinuities and on a MEMS pressure sensor for the measurement of shape and relatively large deflection are presented. U. P. Kumar : N. K. Mohan (*) : M. P. Kothiyal Applied Optics Laboratory, Department of Physics, Indian Institute of Technology Madras, Chennai , India nkmohan@iitm.ac.in Keywords Multiple wavelength. Phase shifting. Interferometry. TV holography. Surface profiling. Fringe analysis Introduction Characterization of deformation and surface shape is an important parameter in quality testing of Microsystems such as Micro-Electro-Mechanical Systems (MEMS) in view of the functionality, reliability and integrity of the components [1 3]. Interferometry or TV holography (TVH) based on single wavelength configuration offers excellent resolution and high sensitivity for metrology applications. In phase shifting interferometry (PSI), a serious limitation to their use is that the surface profile discontinuities of less than half a wavelength only can be measured unambiguously. The approaches adopted to overcome this kind of problem are: twowavelength phase shifting interferometry (TWPSI) [4 6], scanning white light interferometry (SWI) [7, 8], spectrally resolved white light interferometry (SRWI) [9, 10], and multiple wavelength phase shifting interferometry (MWPSI) [10 13]. In TV holography, the single wavelength configuration suffers from overcrowding of fringes for large deformation that sets a limitation due to speckle decorrelation for quantitative fringe analysis. Further shape can not be determined when single wavelength

2 J Opt (October-December 2011) 40(4): is used. Two wavelength electronic speckle pattern interferoemty (ESPI) [14], and multiple wavelength techniques for deformation and shape measurement [15] have been used to overcome these problems. Multiple wavelength techniques can be applied in (a) sequential [13 15], or (b) simultaneous [12] mode of operation. Regular single-chip monochromatic CCD cameras can be used for sequential illumination method. For simultaneous recording of interferograms a three-chip or a single-chip colour CCD cameras is required. Maximum resolution will be achieved by using 3-chip colour CCD. For cost reasons, however, single chip colour camera is used for the present investigation. In this paper we demonstrate a red-green-blue (RGB) wavelength microscopic TV holography and interferometry for 3-D surface profile and deflection measurements. The interferograms are stored simultaneously using a single-chip colour CCD camera. Thus the data acquisition procedure is as simple as single wavelength case. The colour RGB interferograms are decomposed into its monochromatic components. An 8-step phase shifting algorithm which is suitable for RGB wavelength analysis is used for phase evaluation at individual wavelengths [13, 15]. A fringe order method which can provide the resolution of phase shifting interferometry is used for surface profiling on an etched silicon sample with microstructures. Relatively large deflection and shape of a circular MEMS pressure sensor is measured at effective wavelength using phase subtraction method. Red-Green-Blue (RGB) wavelength microscopic interferometric system The multiple wavelength (RGB) interferomeric arrangement shown in Fig. 1 is used for the measurements. He-Ne (1 1 =632.8 nm, 10 mw), frequency doubled Nd:YAG (1 2 =532 nm, 50 mw) and He-Cd (1 3 =441.6 nm, 10 mw) lasers are used in the system. The beams are expanded and collimated using a spatial filtering (SF) setup and a 150 mm focal length collimating lens (CL). An iris in front of the lens allows adjusting the size of the collimated beam, while the variable neutral density filters (VND) in the setup help to control intensity of the beams. Shutter (S) in front of the lasers allows to switch over from one wavelength to other wavelength for storing the images. The collimated laser beam illuminates the micro specimen under study and a reference mirror Fig. 1 Schematic of a multiple wavelength (RGB) interferometric system: S, Shutter; VND, Variable neutral density filter; M, Mirror; BS, Beam splitter; SF, Spatial filter; CL, Collimating lens; NDF, neutral density filter; A, Amplifier; PZT, Piezo electric transducer; DAQ, Data acquisition system

3 178 J Opt (October-December 2011) 40(4): via a beam splitter (BS) simultaneously. The specimen is mounted on a 3-axis stage for alignment. The microscopic imaging system consists of a Thales-Optem zoom 125C long working distance microscope (LDM) with an extended zoom range and a JAI BB-500GE 2/3" GigE vision camera. It is a color progressive scan camera with 5 million pixels resolution and GigE Vision interface. These are single-chip colour sensors which contain the primary colours red, green, and blue and are used in most single-chip digital image sensors used in digital cameras to create a color image. It has 2456(H) X 2058(V) active pixels with a 3.45 μm square pixel. The camera is interfaced to PC with NI PCIe-8231 card. The Zoom LDM provides a 12.5:1 zoom ratio, at working distance of 89 mm with 1.0X objective. A PZT driven reference mirror is used for introducing the phase shifts between the object and reference beams. The PZT is driven by an amplifier which is interfaced to a PC with a DAQ (NI6251) card. The reflected beams from the smooth micro-specimen and the reference mirror for each wavelength are recombined coherently onto the CCD plane. The interfeograms corresponding to each wavelength are recorded simultaneously using the colour CCD. The phase step produced by a PZT is set at 90º for 1 2 =532 nm. The same motion of the PZT introduces a phase-step miscalibration at the other wavelengths. Almost perfect compensation can be obtained by the use of the 8-step algorithm [15, 16]. LABVIEW based programs suitable for colour CCD camera have been developed for visualization of fringes and storing the phase shifted frames. Theory Fringe order method for the measurement of large discontinuities on smooth surfaces In phase shifting interferometry (PSI), we record the phase shifted frames with the intensity distribution given as I in ¼ I o ð1 þ Vcosðf i þ ðn 1Þa i ÞÞ ð1þ where I o is the bias intensity, f 1 is the phase, n is the frame number, and α i is the phase shift for wavelength 1 i given by α i =(1 2 /1 i ) π/2. Using the 8-phase step algorithm [15, 16], the phase distribution can be written in terms of arctan function as f i ¼ arctan I i1 5I i2 þ 11I i3 þ 15I i4 15I i5 11I i6 þ 5I i7 þ I i8 I i1 5I i2 11I i3 þ 15I i4 þ 15I i5 11I i6 5I i7 þ I i8 ð2þ The surface profile phase f i is governed by the following equation f i ¼ 4ps i z ð3þ where wavenumber σ i =1/1 i. The profile height less than 1 i /2 can be measured unambiguously. The variation of ϕi with σ i is linear in Eq. 3. Since we have data for three wavelengths, it is possible to adjust the wrapped phase data at any pixel such that they lie on a best fit line by addition or subtraction of multiples of 2π. The slope of this line gives the absolute height at the pixel as z a ¼ 1 4p Δ f Δs ð4þ The value of z a obtained from Eq. 4 is less precise but it is quite close to the actual value. The fringe order can be determined from the local height value at each pixel and used to correct the single wavelength phase. An improved ambiguity-free phase with precision of phase shifting interferometry can be expressed as Φ i ¼ f i 2p round f i 4ps i z a ð5þ 2p The function round () gives the nearest integer. An improved value with resolution provided by the phase shifting technique can be obtained as z ¼ l i 4p Φ i ð6þ Thus the fringe order method helps to increase the measurement range and to retain the single wavelength resolution of the surface profile of an object.

4 J Opt (October-December 2011) 40(4): Effective wavelength analysis for shape and deformation measurement on rough surfaces For the quantitative evaluation of shape and deformation on rough surfaces, we store separately phase shifted frames at the wavelengths 1 i (i=1, 2, 3) before and after loading the specimen. The phase shifted intensity distribution for the wavelengths 1 i before and after deformation can be expressed as I B in ¼ I o 1 þ V cos f B i þ ðn 1Þa i ð7þ I A in ¼ I o 1 þ V cos f A i þ ðn 1Þa i ð8þ where f B i ; f A i ¼ f B i þ Δ f i are the phases, B and A represent the state of the object before and after deformation, Δf i is the additional phase change due to the object deformation. The phases f B i ; f A i are evaluated using the 8-step Eq. 2. The evaluated individual wrapped phase distributions f B i and f A i is random, hence no fringes can be observed. The subtraction of the phases generated before and after loading the object at each wavelength yields the single wavelength wrapped phase, which is governed by the following equation Δ f i ¼ f A i f B i ¼ 4p w ð9þ l i where w is out-of-plane deformation. The single wavelength procedure does not reveal the shape of the object under study. The use of multiple wavelengths reveals the information pertaining to surface shape (z) of an object. By subtracting the phases f B i, shape before deformation can be obtained which is governed by the following equations: f 1 B f 2 B ¼ 4p Λ 1 z; f 2 B f 3 B ¼ 4p Λ 2 z; f 1 B f 3 B ¼ 4p Λ 3 z ð10þ where Λ 1 ¼ l 1 l 2 jl 1 l 2 j, Λ 2 ¼ l 2 l 3 jl 2 l 3 j, and Λ 3 ¼ l 1 l 3 jl 1 l 3 j are effective wavelengths. Similarly shape after deformation can be obtained using the phases f A i that represent the information pertaining to deformation and shape as f A 1 f A 2 ¼ 4p Λ 1 ðw þ zþ; f A A 2 f 3 ðw þ zþ; f A 1 f A 3 ¼ 4p ¼ 4p Λ 2 Λ 3 ðw þ zþ ð11þ The deformation component w at reduced sensitivity can be measured using Eqs. 10 and 11. Thus the effective wavelength analysis yields the information pertaining to deformation and shape. Experimental results 3-D surface profiling on smooth surface using fringe order method Figure 2(a) shows the colour CCD image of tilt fringes stored simultaneously at R,G,B wavelengths. The dimensions of the colour image are 2456X2058X3. Each pixel contains the information regarding the individual wavelengths. It is then separated into its monochrome components of dimensions 2456X2058. The decomposed components at 1 1, 1 2, and 1 3 are shown in Fig. 2(b). Similarly all the phase shifted patterns stored under simultaneous illumination condition are decomposed and processed separately. Figure 2(c) shows the wrapped phase maps generated for each wavelength using 8-step equation (Eq. 2). Figure 3 shows the experiential results on an etched silicon sample with several stepped structures. Figure 3 (a) shows the simultaneously recorded RGB wavelength interferogram. The colour interferograms thus recorded are separated into its monochromatic components. The fringe pattern and wrapped phase maps evaluated at 1 1 =632.8 nm wavelength obtained following the procedure explained above are shown in Fig. 3(b) and (c) respectively. Similarly phase maps can be obtained at 1 2, and 1 3. The wrapped phase maps thus evaluated can be used to increase the unambiguous range in two ways: (a) Phase Subtraction Method (PSM) [13], and (b) Fringe Order Method (FOM) [12, 13]. In phase subtraction method, phase maps at individual wavelengths are subtracted to generate effective wavelength phase map. The profiles measured at effective wavelengths are noisy due to the fact that the signal-to-noise ratio (SNR) increases with the wavelength used for measurement (i.e. error amplification effect) [4, 13]. Where as the fringe order method ( Fringe order method for the measurement of large discontinuities on smooth surfaces ) can provide surface profile with the resolution of single wavelength and it can extend the measurement range of the interferometer. Figure 3(d) shows the ambiguity removed 3-D profile using

5 180 J Opt (October-December 2011) 40(4): Fig. 2 Flow chart for RGB wavelength interferometric fringe analysis: a RGB wavelength interferogram, b interference patterns, and c wrapped phase maps at individual wavelength Fig. 3 3-D Surface profile analysis using the fringe order method: a simultaneously recorded RGB wavelength interferogram, b interferogram at 1 1, c wrapped phase map at 1 1, d 2mπ ambiguity corrected single wavelength 3-D surface profile of an etched silicon sample using nm phase data, and e line scan which shows a profile height of 1.12 μm

6 J Opt (October-December 2011) 40(4): fringe order method for 1 1 =632.8 nm. The profile height measured is 1.12 μm. The profile shown in Fig. 3(e) has the usual smoothness of single wavelength phase shifting interferometry. Measurement of shape and deflection on rough surface using effective wavelength analysis Initially we have carried out experiments on a flat mm 2 specimen (z=0). Following the simultaneous recording procedure, eight phase shifted frames before and after tilting the specimen are stored in the PC. Figure 4 shows the procedure for multiple wavelength speckle fringe analysis for shape and deformation measurement. The speckle patterns stored by simultaneously illuminating the object with red and green wavelengths are shown in Fig. 4 (a). These fames are then decomposed in to its monochromatic components which are shown in Fig. 4(b). The speckle patterns at single wavelength before and after loading are subtracted to generate speckle correlation fringes and are shown in Fig. 4(c). The speckle phases at individual wavelengths calculated using 8-step method (Eq. 2) are shown in Fig. 4(d). The wrapped phase map generated at each wavelength by subtracting the speckle phase before and after loading are shown in Fig. 4(e). While calculating the wrapped phase maps, a sine-cosine median filtering with 3 3 window is used to reduce the noise associate with raw phase maps. The phases shown in Fig. 4 (d) can be used to extract the shape before and after loading the difference of which results in a resultant deformation at effective wavelength. Experiments were also carried out on a silicon based circular MEMS pressure sensor of diameter 1.5 mm for shape and deflection fringe analysis by applying the pressure externally. Following the same procedure as explained above, eight phase shifted frames are stored Fig. 4 Flow chart for multiple wavelength speckle fringe analysis: a multiple wavelength (red plus green) speckle patterns before and after loading, b speckle patterns after decomposition, c tilt fringes, d speckle phase maps at 1 1 and 1 2, and e phase maps at 1 1 and 1 2 respectively

7 182 J Opt (October-December 2011) 40(4): Fig. 5 Deflection fringe using multiple wavelengths on a circular MEMS pressure sensor of diameter 1.5 mm and thickness 25 μm: a multiple wavelength specklogram at P=50 kpa, b deflection fringes at 1 1, c deflection fringes at 1 2, and d unwrapped line scan profiles at individual wavelengths and are identical as expected before and after loading the sensor. Figure 5(a) shows multiple wavelength deflection correlation fringes simultaneously recorded at P=50 kpa. The deflection fringe patterns after decomposition at 1 1 =632.8 nm and 1 2 =532 nm are shown in Fig. 5(b) and (c) respectively. The corresponding unwrapped deflection line scan profiles at individual wavelengths are shown in Fig. 5(d). The deflection profiles are identical as expected and the measured deflection at the center of the sensor is 1.75 μm. Similarly the applied pressure is increased in a controlled manner and corresponding data is analyzed Fig. 6 Multiple wavelength fringe analysis on a circular MEMS pressure sensor of diameter 1.5 mm and 25 μm thickness at P=150 kpa: overcrowded fringes at a 1 1, b 1 2 ; wrapped phase maps at 1 1 =3.34 μm c before deflection, d after deflection, e wrapped phase map obtained by subtracting the phase maps in Fig. 6(c) and 6(d); f unwrapped line scan along the central x-axis; Profile-A represents shape profile before deflection, while Profile-B shows the deflection along with the shape profile. Profile-C shows the resultant deflection profile. It is however, necessary to make such that the effect of cross talk between the three channels of the CCD camera is eliminated or reduced

8 J Opt (October-December 2011) 40(4): for deflection measurements. Relatively large pressure results in overcrowding of fringes. The overcrowded fringes at P=150 kpa at 1 1 =632.8 nm and 1 2 =532 nm are shows in Fig. 6(a) and (b) respectively. Because of the large deflection and high frequency of the wrapped phase, quantifying the data is difficult. The effective wavelength analysis ( Effective wavelength analysis for shape and deformation measurement on rough surfaces ) helps to overcome such problems associated with single wavelength data. The effective wavelength (Λ 1 =3.34 μm) phase map obtained by subtracting the wrapped phase maps at individual wavelengths 1 1 and 1 2 are shown in Fig. 6(c) to (e). The initial phase maps ( f i B ) at 1 1 and 1 2 are subtracted (Eq. 10) to yield shape before deflection (Fig. 6(c)) and the final phase maps ( f i A ) are subtracted (Eq. 11) for generating shape after loading (Fig. 6 (d)) respectively. The difference of the phase maps shown in Fig. 6(c) and (d) yields deflection phase at effective wavelength, Λ 1 =3.34 μm, which is shown in Fig. 6(e). The line scans along the central x- axis are given in Fig. 6 (f). The line scan profile-a represents the shape of the sensor before deflection. It indicates that the silicon membrane is projecting out about 1.8 μm with reference to the silicon wafer surface. The line scan profile-b represents the deflection along with the shape, while profile-c gives the deflection profile of the sensor. Conclusions We have demonstrated a red-green-blue wavelength system using a single-chip colour CCD for deflection and 3-D surface profile analysis. Interference patterns at all the wavelengths are recorded simultaneously using color CCD camera which makes the data acquisition process faster than the case when monochromatic camera is used. Thus the data acquisition and phase evaluation procedures are as simple as in case of single wavelength method. The use of 8-step algorithm simplifies the application of phase shifting technique in the multiple wavelength system. It also offers great flexibility in sensitivity and measurement range by an appropriate choice of the different wavelengths. The results of this study can be used when the three lasers are replaced by a white light source making the set up simple. Acknowledgement This work is supported by Defense Research and Development Organization (DRDO). References 1. W. Osten, Optical inspection of microsystems (CRC, Boca Raton, 2007) 2. L. Yang, P. Colbourne, Digital laser micro-interferometer and its applications. Opt Eng 42, (2003) 3. N. Krishna Mohan, P.K. Rastogi, Recent developments in interferometry for microsystems metrology. Opt Lasers Eng 47, (2009) 4. K. Creath, Step height measurement using two-wavelength phase-shifting interferometry. Appl Opt 26, (1987) 5. J. Schmit, P. Hariharan, Two-wavelength interferometry profilometry with a phase-step error - compensating algorithm. Opt Eng 45, (2006) 6. U. Paul Kumar, B. Bhaduri, N. Krishna Mohan, M.P. Kothiyal, Two wavelength microinterferometry for 3-D surface profiling. Opt Lasers Eng 47, (2009) 7. P. de Groot, L. Deck, Three-dimensional imaging by sub- Nyquist sampling of white-light interferograms. Opt Lett 18, (1993) 8. P. de Groot, L. Deck, Surface profiling by analysis of white-light interferograms in the spatial frequency domain. J Mod Opt 42, (1995) 9. P. Sandoz, G. Tribillon, H. Perrin, High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferogram. J Mod Opt 43, (1996) 10. S.K. Debnath, M.P. Kothiyal, Experimental study of the phase-shift miscalibration error in phase shifting interferometry: use of a spectrally resolved white-light interferomete. Appl Opt 46, (2006) 11. Y.-Y. Cheng, J. Wyant, Multiple wavelength phase-shifting interferometry. Appl Opt 24, (1985) 12. A. Pfortner, J. Schwider, Red-green-blue interferometer for the metrology of discontinuous structures. Appl Opt 42, (2003) 13. U. Paul Kumar, N. Krishna Mohan, M.P. Kothiyal, Measurement of discontinuous surfaces using multiple wavelength interferometry. Opt Eng 48, (2009) 14. E. Hack, B. Frei, R. Kästle, U. Sennhauser, Additive-Subtractive two-wavelength ESPI contouring by using a synthetic wavelength phase shift. Appl Opt 37, (1998) 15. U. Paul Kumar, N. Krishna Mohan, M.P. Kothiyal, Deformation and shape measurement using multiple wavelength microscopic TV holography. Opt Eng 48, (2009) 16. J. Schmit, K. Creath, Windows function influence on phase error in phase shifting algorithms. Appl Opt 35, (1996)