Recent Advances in Mechatronics - Ryszard Jabonski et al (Eds) Episode 2 Part 8 pot

664 M. Kretkowski, H. Suzuki, Y. Shimodaira, R. Jabłoński estimated by least square sum analysis involving spectral data and values obtained from camera CCD sensor for each color reference Introduction For accurate color reproduction there is a need of developing new tools for calibrating a digital camera system capable of reproducing high fidelity colors for telemedicine, internet shopping, industrial design and other high accuracy color reproduction demanding applications The camera is equipped with three filters S1, S2 and S3, which correspond to red, green and blue band These filters have relative spectral sensitivity similar to primary color sensitive cones in human eye (Fig 1.) Macbeth ColorChecker® Chart is used to determine numerical color description for reference As an illuminant there is a CIE Daylight 65 (D65) standard used Under this certain conditions, automatic method of calibration with use of an integrated spectrometer inside the camera based on a fiber optic measuring probe has been developed Relative transmittance Wavelength [nm] Fig.1 Filter spectral characteristics Measured color is represented by the tristimulous XYZ values [1] Color captured by the camera is represented by S1, S2, S3 values, corresponding to pixel value under each filter acquisition To provide high fidelity color reproduction, a conversion matrix between XYZ and S1, S2, S3 values must be obtained by means of least square sum analysis [2] XYZ camera principle For total description of color there can be used so called tristimulous values XYZ [1] A digital still camera with output containing these Automatic color calibration method for high fidelity color reproduction digital  665 values, supported by proper filters and equipped with internal spectrometer is able to reproduce high fidelity colors in the same way as human eye would perceive it Figure shows principle of the camera Light passing through the lens is split by a semi-transparent mirror Part of the light reflected by the mirror is used for spectral measurement, while light passing through is projected onto CCD imaging device with S1, S2, S3 filters put on its way Fig XYZ camera principle Basic principle is to take three pictures of photographed scene under each filter acquisition This gives three layer image called: “S1, S2 and S3 image” The spectrometer is used for calibration of the camera With an algorithm described further, by mathematical conversion S1, S2, S3 image is converted to XYZ image which describes colors contained in the scene in XYZ color space [1] which is a base for any other color representation 666 M. Kretkowski, H. Suzuki, Y. Shimodaira, R. Jabłoński Proposed calibration algorithm Spectral data is collected automatically from Macbeth Chart’s 24 colors by fiber optic probe positioned over picture area along the x and y Taking the illuminant by reflecting plate White balancing Macbeth’s Chart picture taken on a contrasting Background Color calibration Threshold procedure Color fields position estimation Axis calibration Dark current estimation Fiber optic‘s positioning system Conversion matrix XYZ Output Spectrum Measurement Lens shading characteristics axes (Fig 3.) The positioning mechanism is built inside the camera and its coordinate system has been calibrated with picture area This gives a possibility of acquiring spectral data from any point of the photographed scene Described algorithm uses image processing for recognition of each color on Macbeth Chart and to find coordinates for spectrometer’s probe to be positioned and perform measurement of each color automatically Fig Block scheme of calibration algorithm Calibration starts with acquiring illuminant data (Fig 3.) by perfect reflecting plate The Macbeth Chart then is placed into the scene and color pads are recognized and measured XYZ and S1, S2, S3 data is tabulated and stored into memory Basic relation between the values is:  X   a11 Y  =  a    21  Z   a31    a21 a22 a32 a31   S1  a 23   S    a33   S    (1) Automatic color calibration method for high fidelity color reproduction digital  667 The color difference between reference and values obtained from calibrated camera, is well described by CIE Lab color space derived from XYZ [1] The color difference �E principle which describes accuracy of color reproduction can be expressed with equation (2) (CIE 1932) Where ∆E = ( L1 − L ) + ( a1 − a ) + (b1 − b ) ( 2) Li is luminance of compared colors and ai, bi are chroma coefficients However at present CIE 2000 is used, to describe �E in more perceptually uniform color difference representation Results and discussion The calibration of the spectrometer is most important in order to develop a conversion matrix giving the smallest color difference between measured XYZ color and X’Y’Z’ obtained from S1, S2 and S3 [2] Other major influencing factor is shading of the camera lens (winietting) Present results show strong dependency between F number and color difference (Tab 1.) As we observed color difference decreases as the F number increases Table Color difference and F number 2.8 F of the camera lens Color difference (average) 2.04 CIE 2000 5.6 1.35 1.13 This is caused by shading characteristics of whole optics including camera lens, mirror, fiber optics and spectrometer spectral response To improve the accuracy of reproduction and reduce �E, amount of light reflected from the semi-transparent mirror must be increased to provide better signal to noise ratio of the spectrometer Above facts lead to conclusion that accurate color reproduction for still digital camera requires careful calibration Proposed algorithm uses color reference and includes various factors for maximum performance However in further development it will be investigated for possibility of calibration using colors of the photographed scene as a reference References [1] R.W.G Hunt “The Reproduction of Colour” ISBN (1995) [2] T Ejaz, T Horiuchi, G Ohashi, Y Shimodaira IEICE Trans Electron., E89-C (2006) Coherent noise reduction in optical diffraction tomography A Pakuła*, T Kozacki Warsaw University of Technology, Institute of Micromechanics and Photonics, Sw A.Boboli St., 02-525 Warsaw, Poland Abstract Optical Diffraction Tomography (ODT) is the method for characterization of 3D distribution of refractive index in micro optical elements The 3D distribution is obtained from several measurements taken for different object angular orientation taken by means of laser interferometry Unfortunately the interferometry as a coherent technique suffers from undesirable coherent noise in measurements results Additionally the rotation of a measured object increases the noise influence on the quality of refractiveindex reconstruction due to its amplification in the object area In this paper we propose the coherent noise suppression technique The technique involves modification of ODT setup configuration by introducing off center object rotation and applying a modified numerical algorithm of tomographic reconstruction The algorithm modification involves introduction of numerical imaging and detection of element position from its diffraction spectrum The received results of noise reduction are shown through numerical simulations and experiments involving optical single mode fiber measurements Introduction The recent rapid growth of microelements with three-dimensional phase distribution, photonics structures and materials (e.g photonics crystal fibers, GRIN lenses etc.) which are vastly used in photonics devices results in need for fast, nondestructive method of 3D refractive index distribution The ODT is the method suitable for such measurement tasks [1-6] Coherent noise reduction in optical diffraction tomography 669 Using classical interferometry 2D refractive index distribution, integrated along optical axis, is obtained for variable angular object orientation For every single object angular orientation (range within 1°÷180°) interferogram is recorded and analyzed Then the 3D refractive index distribution is obtained using tomographic reconstruction algorithm The results obtained by ODT have been recently improved by introduction of numerical procedure of refocusing to the best focus plane and sample radial run-out correction algorithm [6], although there is still unsolved problem of coherent noise, especially if measured sample introduces slight changes (order of 10-3 or lower) in refractive index Coherent noise reduction technique In principle the ODT involves sample rotation along the axis in the object centre This causes the single speckle magnification during the tomographic algorithm what results in semicircular shape in reconstructed refractive index map (Fig 1) Fig 1: Coherent noise influence on refractive index reconstruction by tomographic algorithm – multimode optical fiber [5] Introduction of substantial radial run-out into sample rotation process along with sinogram correction correlation technique allows the coherent noise influence to be reduced According to simulation results (simulated object: refractive index distribution: step ∆n=0.01, diameter φ=100λ) the optimal radial run-out range is 0.75φ - 1.25φ, Fig In this range the RMS factor decreases and the S/N ratio rises – Fig Although introducing run-out into measurement, according to simulations, is a significant benefit, it gives some experimental difficulties Such a 670 A. Pakuła, T. Kozacki  modified setup requires larger measurement field of view, which results in lower magnification Additionally the defocusing of the sample is inserted by the sample rotation For decreasing the influence of factors mentioned above the numerical sinogram correction and refocusing to the best focus plane algorithms need to be applied a) b) Fig 2: Simulations results of tomographic numerical reconstruction: (a) without radial run-out (b) radial run-out - 2φ a) b) Fig 3: Simulations’ results due to the sample’s radial run-out: (a) RMS factor, (b) S/N ratio Experimental technique Experimental tomographic setup is based on classical Mach – Zehnder interferometer setup (Fig 4.) He – Ne laser beam formed by microscope objective (OB1) is spitted into reference and object beams by a coupler (FC) The measured object (O) submerged in immersion liquid (n633=1.4584) is illuminated by a plane wave and rotated during the measurement The imagining system is focused in the sample’s centre area The measurement is performed in the following steps For every sample angular orientation interferogram are grabbed and analyzed forming phase pro- Coherent noise reduction in optical diffraction tomography 671 jection images data set Finally from this data set 3D refractive index map is reconstructed by means of thomographic reconstruction algorithms As a proof of principle of our method the experiment involving characterization of refractive index distribution of single mode telecommunication fiber (SMF 28) was performed (core diameter 8.2 m, cladding diameter 125 m, ∆n=0.0053) [7] The experimental run-out was 129.2m RS O PC L BS D λ/2 OB2 OB4, OB5 OB3 λ/2 S FC OB1 Fig 4: Experimental tomographic setup: S – He-Ne laser, λ/2 – halfwave plate, OB1, OB2, OB3 – fiber coupling objectives, FC – fiber coupler, OB4, OB5 – microscopic imagining objectives, BS – beam splitter, L – camera objective, O – measured object, RS – rotation stage, D – detector, PC – central unit a) b) Fig 5: Results of measurement of single mode fiber (1 pix = 0.2315 m): (a) reconstruction and cross section without radial run-out, (b) reconstruction and cross section with 129 m radial run-out 672 A. Pakuła, T. Kozacki  The core diameter and difference of average refractive index between the core and the cladding of the reconstructed fiber from measurements without and with radial run-out are equal adequately: φ = 9.03 m (39 pix), ∆n=0.006 and φ=9.26 m (40 pix) (elliptical deformation occurs), ∆n=0.005 However, as it is shown in Fig 5b the semicircular shape in tomographic reconstruction which has its origins in the coherence noise is removed by introduction of radial run-out the proposed technique introduces deformation of the measured object The full uncertainty analyses for the case of the modified procedure have to be performed Conclusions The novel method of reduction of the coherence noise influence on tomographic reconstruction reduction was proposed and verified by the numerical simulations and the experiment References [1] M Kujawinska, P Kniazewski, T Kozacki “Enhanced interferometric and photoelastic tomography for 3D studies of phase photonics elements”, Proc of the Symposium on Photonics Technologies for 7th Framework Program, 467- 471, Wroclaw, 2006 [2] W Gorski “Tomographic microinterferometry of optical fibers”, Opt Eng 45 (12), 2006 [3] B.L Bachim, T.K.Gaylord „Microinterferometric optical phase tomography for measuring small, asymmetric refractive-index differences in the profiles of optical fibres and fiber devices”, App Opt., Vol 44, 2005 [4] P.Guo, A.J.Devaney „Comparison of reconstruction algorithms for optical diffraction tomography”, J Opt Soc Am A., Vol 22, 2005 [5] P.Kniazewski, W Gorski, M Kujawinska „Microinterferometric tomography of photonics phase elements” Proc SPIE Vol 5145, 2003 [6] T.Kozacki, M.Kujawińska, P.KniaŜewski „Investigation of limitations of optical diffraction tomography”, Opto-Electron Rev., 15, 2007 [7] Cornig Inc “Cornig SMF 28 Optical Fiber Product Information”, 2002 On micro hole geometry measurement applying polar co-ordinate laser scanning method R Jabłoński, P Orzechowski Warsaw University of Technology, Institute of Metrology and Measurement Systems, Sw A Boboli Street 8, Warsaw, 02-525, Poland Abstract The measurement of long micro hole is often problem in contemporary technology Particularly difficult is the measurement of micro holes of the length to diameter (l/d) ratio higher than 10 The paper presents the new measurement method based on polar co-ordinate scanning with photon counter as a detector When cylindrical micro hole is scanned with elliptical laser beam, and the hole axis and measurement device axis is not coaxial, the measurement results can be ambiguous and dependent on a distance between axes This problem can be solved by expansion of results series into a Fourier series The ratio of zeroth and first order coefficient of Fourier expansion, strongly depends on the distance between axes Introduction Contemporary technologies make possible the production of small and long holes The commonly used parameter in micro hole technology is length to diameter ratio (l/d) Holes made by photolithographic technologies (LIGA, DRIE), could have smallest dimensions of single micrometers, but its length is limited to 0,5 mm (DRIE), or mm (LIGA) Another technologies like laser drilling, or EDM, ECM make possible the production of micro holes, but l/d ratio is limited for diameter smaller than approx 30 m [1] Measurement techniques, applied for such small objects are mainly microscope methods [2], but also special contact methods [3], volumetric, and diffraction methods Measurement becomes very difficult when the hole is small and long (l/d>10) The new method presented 678 R. Jabłoński, P. Orzechowski of hole and measuring device The results of Fourier analysis can be used either to set the correct position of hole during the measurement, or to determine corrections used for further calculation of measurement results 0,776 0,771 0,766 0,761 first to zeroth 0,756 harmonic ratio [-] 0,751 0,746 20 0,741 -20 0,736 -40 -20 20 axes shift in x-direction [um] -40 axes shift in ydirectio n [um] Fig The first to zeroth harmonic ratio for various distances between nominal hole axis and nominal measurement stand axis The above mentioned systematic error is not explained yet, and it will be the subject of further investigations References: [1] B Odom, Manufacturing Engineering 126/2 (2001) 88-102 [2] P Waurzyniak, Manufacturing Engineering 133/1 (2004) 107-114 [3] M Yamamoto, I Kanno, S Aoki, Proceedings of 30-th Conference on MEMS (2000) 217-222 [4] R Jabłoński, P Orzechowski, Precision Engineering 30 (2006) 180184 Silicon quantum detectors with large photosensitive surface A Baranouski (a), A Zenevich (b) , E Novikov (b) (a) Institute of Applied Physical Problems, Kurchatov str., 7, Minsk, 220064, Republic of Belarus (b) Higher state college of communication, Skorina str 8/2, Minsk, 220114, Republic of Belarus Abstract Semiconductor light detectors are the part of vision and image processing systems Pulse amplitude distribution of silicon avalanche photodiodes with photosensitive surface mm2 is investigated using measurement computer system Amplitude characteristics in the photon-counting mode are studied depending on the supplied overvoltage, laser intensity and photosensitive surface area It is shown that changing the supplied overvoltage and photosensitive surface area causes increase / decrease of the peaks number on pulse-amplitude distribution curve due to several microplasmas in the region of space charge Introduction Computer vision and pattern recognition systems require application of various combinations of optical sensors, laser rangers, microwave sensors In this case very simple and inexpensive solution is utilization of chargecoupled devices, manufactured as multiple-unit matrices, and photodetectors with large area of the photosensitive surface Progress of microelectronics in the area of such image registration devices development ensures combination of the high resolution and high rate of imaging with the possibility for registration of separate photons A single-quantum registration or the photon counting method is the most frequently used for registration of the optical radiation with the extremely week intensity by application of the solid-state photodetectors with the internal amplification [1] 680 A. Baranouski, A. Zenevich, E. Novikov An ordinary silicon photodetectors with large photosensitive surface areas possess sufficiently high thermoelectric noise, thereby preventing application of the photon counting mode at room temperatures Hence, the purpose of this work is to show the possibility of realizing the photon counting mode using photodetectors with photosensitive surface area up to several square millimeters with a view to register very low intensity light Experiment and discussion The avalanche photodetectors with a mm2 photosensitive area were used They featured a metal–resistive layer–semiconductor structure [2] based on single-crystal silicon substrate with a Ω⋅cm resistivity Thin undoped zinc–oxide film of n-type conductivity (d=30 nm, and ρ = 107Ω cm) was locally formed, ensuring the formation of an iZnO–Si heterojunction and acting as a resistive layer, and ZnO : Al film (d� 0.5 µm, and ρ = 10-3 Ω cm) as a transparent conducting electrode The photon–counting mode was realized with a passive avalanche quenching circuit [2] The photodetector acts similarly to a Geiger-Muller quantum counter Avalanche breakdown voltage Uav of photodetectors equals 76.8 V So called overvoltage ∆U = Us − Uav (Us – supply voltage) was used to analyze amplitude characteristics under variation of experiment conditions Semiconductor laser with λ = 0.68 µm and focusing system were utilized to light the photosensitive area completely and in part Hardware and software package comprising 100 MHz analog-digital converter was used for registration of pulse amplitude characteristics in the real-time mode Pulses with duration 1.0-1.1 µs and rise time less than 100 ns were observed Their amplitude A depended on supplied overvoltage The pulse is called dark when avalanche breakdown initiated by electron as a result of thermal excitation And the pulse is called signal when electron generated via photon absorption Amplitude distribution of dark pulses was measured as a function of supply overvoltage (Fig 1) The number of peaks on amplitude distribution increased as supply voltage rose The similar picture was observed for the total process of dark and signal pulses The number of peaks depends on homogeneity of photosensitive area and charge carriers multiplication region Heterogeneities have different gain and account for avalanche pulses with different amplitude Such heterogeneities in space charge region are called microplasmas Silicon quantum detectors with large photosensitive surface 681 Mean M and variance D were calculated versus supplied overvoltage for dark and signal pulses to characterize statistics of pulse amplitude (Fig 2) 250 p(A), V-1 200 150 100 50 0.005 0.010 0.015 0.020 0.025 A, V Fig Amplitude distribution of dark pulses for three supply overvoltages (1 - ∆U = –0.3 V; – ∆U = –0.1 V; – ∆U = 0.1 V) Fig Mean and variance of avalanche pulse amplitude versus supply overvoltage (1, – dark pulses, 2, – signal and dark pulses) 682 A. Baranouski, A. Zenevich, E. Novikov The behavior of statistical parameters is similar in presence and absence of laser irradiation The variations of mean and variance not exceed more then 2-3 times In this case operating mode is chosen according to the number of peaks and their magnitude Demonstrate this fact Amplitude distributions of avalanche pulses demonstrated shape changing as we varied laser stimulation area on photosensitive surface (Fig 3) 250 200 p(A), V-1 150 100 50 0.005 0.010 0.015 0.020 0.025 A, V Fig Amplitude distribution of avalanche pulses for ∆U = V (1 – dark pulses, 2, – laser stimulation in different regions of photosensitive surface area) Each peak magnitude of the amplitude distribution depended on the laser beam position on the photosensitive area By measuring number, position and magnitude of peaks it is possible to evaluate light intensity on the photosensitive surface Conclusion Amplitude characteristics of avalanche pulses in silicon quantum detector with large photosensitive surface have been investigated for the purpose of using the devices in automatic vision systems operating in the photoncounting mode It was shown that imperfections in light detection and amplification regions resulted in variation of avalanche pulse amplitude Therefore, such photodetectors containing several multiplication regions Silicon quantum detectors with large photosensitive surface 683 may be used in the pattern recognition system under very low light intensity References [1] J Fraden “Handbook of modern sensors: physics, designs, and applications” Springer-Verlag, New York, 2004 [2] I R Gulakov, V B Zalesskii, A O Zenevich, T R Leonova, Instruments and experimental techniques 50, (2007) 249 Fizeau interferometry with automated fringe pattern analysis using temporal and spatial phase shifting Adam Styk, Krzysztof Patorski Institute of Micromechanics and Photonics, Sw A Boboli St Warsaw 02-525, Poland Abstract The paper presents a novel approach to measure the parameters of quasiparallel plates in a Fizeau interferometer The beams reflected from the front and rear surfaces lead to a complicated interferogram intensity distribution The phase shifting techniques (temporal and spatial) are proposed to process the interferograms and obtain a two-beam-like fringe pattern encoding the plate thickness variations Further pattern processing is conducted using the Vortex transform Introduction The surface flatness of transparent plates is frequently tested in a conventional Fizeau interferometer In case of quasi-parallel plates, however, a common problem is the interference of more than two beams They are reflected from the plate front and rear surfaces and the reference flat Parasitic intensity distribution modulates the two-beam interferogram of the plate front surface [1,2] and makes the application of phase methods for automatic fringe pattern analysis [3-6] inefficient On the other hand parasitic fringes contain the information on the light double passage through the plate Several methods to suppress unwanted fringe modulations are available, for example: index matching treatment on the rear surface of the plate, short-coherence interferometry, grating interferometry, grazing incidence interferometry and wavelength-scanning interferometry [1, 2] In this paper we present preliminary investigations of a novel proposal of processing the interferograms of quasi-parallel optical plates It is based on Fizeau interferometry with automated fringe pattern analysis using temporal 685 the observation that the two-beam interference pattern formed by the beams reflected from the front and rear plate surfaces only can be readily derived from the three-beam interference using temporal phase stepping (TPS) or spatial carrier phase stepping (SCPS) methods The resulting single frame pattern can be processed using the Vortex transform approach [7,8] The phase distribution obtained maps the plate thickness variations Principle and theory of the method The intensity distribution formed by the three interfering beams in the Fizeau cavity can be rewritten as: I = Ar + Af + Ab + Af Ab cos(θ f − θb ) + 2 2 Af Ar cos(θ f − θ r ) + Ar Ab cos(θ r − θb ) (1) Ar, Af, Ab, θr, θf and θb are the amplitudes and phases of the three beams, respectively For notation brevity the (x,y) dependence of all terms has been omitted The goal is to determine the parameters of a quasi-parallel plate such us the front surface phase θf and back surface phase θr using typical fringe pattern analysis methods Using the phase shifting method with a mechanical (PZT) phase shift one obtains the interferograms in the form: I = D + A f Ar cos(θ f − θ r − nδ ) + Ar Ab cos(θ r − θ b − nδ ) , (2) where n = 0,1,2,3, and δ is the phase shift between frames When the amplitudes of the beams reflected from the front and back surfaces are nearly equal (Af ≅ Ab) the terms before cosine terms in Eq are equal as well Using trigonometric identities the intensity distribution becomes:  θ f − θb   θ f + θb  I = D + A f Ar cos   cos − θ r − nδ         (3) A new fringe pattern based on two fringe families multiplied by each other is obtained It can be treated as a two beam interferogram with the bias described by the term D (constant) and the modulation distribution described by the first cosine term The modulation distribution carries the information on the plate optical thickness variations and the main cosine term gives the information on the sum of two surfaces Using conventional techniques for fringe pattern analysis (TPS, SCPS), it is possible to evaluate the information on the optical thickness variations separately 686 A. Styk, K. Patorski Five mutually phase shifted interferograms, Eq 3, acquired with the phase shift δ = π/2 and put into the standard TPS five frame algorithm [9,10] for modulation calculation give the modulation distribution Md in the form: θ Md = A f A r cos    f − θb     (4) The calculated distribution may be treated as a fringe pattern without bias However, in the form presented by Eq it cannot be analyzed due to its highly nonsinusoidal profile as it is a modulus function To overcome this difficulty one can square the Md distribution and obtain: Md = (2 A Ar ) f [1 + cos (θ f ] − θb ) (5) The optical thickness variations of the quasi - parallel plate can be evaluated from Eq As the presented fringe pattern cannot be intentionally modified, only the single frame analysis methods can be applied [7,11] Fringe pattern analysis method In this Section the processing path of the three – beam interference pattern described by Eq is introduced, see Fig Set of phase shifted interferograms Md2 - modulation determination Vortex Transform (VT) Fringe pattern bias removal Information on optical thickness variations of tested plate Fig Three beam interferogram processing path In the first step the set of five to seven mutually phase shifted interferograms (with δ = π/2) is recorded If the TPS technique cannot be implemented, the SCPS technique might be used In this case only one interferogram, with intentionally introduced spatial carrier fringes, is sufficient to evaluate the desired parameters Unfortunately the interferogram processing using the SCPS method provides lower accuracy than the TPS method The next step in the three beam interferogram processing path is to calculate the squared interferogram modulation distribution Md2 This can be performed with a specially derived TPS algorithm with high resistance to Fizeau interferometry with automated fringe pattern analysis using temporal 687 the phase step error [12] Detailed studies of systematic errors of the most common TPS algorithms applied to modulation calculations can be found in [13] The modulation fringe pattern needs to be processed using single frame analysis methods The method presented by Larkin et al [7,8] was chosen for calculations This method, called the Vortex Transform (VT), is based on the two-dimensional Hilbert transform Experimental results Experimental work has been conducted using the Fizeau interferometer with the reference element axially displaced by three PZTs placed along the optical element circumference (diameter of 50 mm) Figure presents a three beam interferogram (one from the set of five phase shifted interferograms) of a microscope cover glass and the calculated squared modulation distribution Md2 Figure shows the quadrature signal of the fringe pattern (Fig 2b) calculated using VT and the wrapped phase distribution with information about plate optical thickness variations a) b) Fig Experimental three - beam interferogram (a) and the calculated squared modulation distribution Md2 (b) a) b) Fig Quadrature signal of the fringe pattern presented in Fig 2b (a) and the calculated wrapped phase distribution (b) 688 A. Styk, K. Patorski Conclusions Preliminary investigations of a novel processing path of interferograms of quasi-parallel optical plates tested in a Fizeau interferometer were presented The processing path is based on the observation that the two-beam interference pattern formed by the beams reflected from the front and rear plate surfaces only can be derived from the three-beam interference using either temporal (TPS) or spatial carrier phase stepping (SCPS) methods The evaluated single frame pattern can be subsequently processed using the vortex transform (VT) approach The phase distribution obtained corresponds to plate optical thickness variations Experimental investigations corroborate the theoretical and numerical findings Acknowledgments The authors want to thank Dr Piotr Szwaykowski for performing the part of measurements and fruitful discussions This work was supported by the grant of the Dean of Faculty of Mechatronics and the statutory founds References [1] P de Groot, “Measurement of transparent plates with wavelengthtuned phase-shifting interferometry”, Appl Opt 39(16), 2658-2663 (2000) [2] K Hibino, B.F Oreb, P.S Fairman, and J Burke, “Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer”, Appl Opt 43(6), 1241-1249 (2004) [3] J Schwider, “Advanced evaluation techniques in interferometry,” Chap in Progress in Optics, E Wolf ed., 28, 271-359, North Holland, Amsterdam, Oxford, New York, Tokyo, 1990 [4] J.E Greivenkamp, and J.H Brunning, “Phase shifting interferometry,” Chap 14 in Optical Shop Testing, D Malacara ed., 501-598, John Wiley & Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore, 1992 [5] K Creath, “Temporal phase measurement methods,” Chap in Interferogram Analysis: Digital Fringe Pattern Measurement, D.W Robinson and G Reid, eds., 94-140, Institute of Physics Publishing, Bristol, Philadelphia, 1993 Fizeau interferometry with automated fringe pattern analysis using temporal 689 [6] D Malacara, M Servin, and Z Malacara, Interferogram Analysis for Optical Shop Testing, Marcel Dekker, Inc., New York, Basel, Hong Kong, 1998 [7] K.G Larkin, D.J Bone, and M.A Oldfield, “Natural demodulation of two-dimensional fringe patterns I General background of the spiral quadrature transform”, J Opt Soc Am A, 18(8), 1862-1870 (2001) [8] K.G Larkin, “Natural demodulation of two-dimensional fringe patterns II Stationary phase analysis of the spiral phase quadrature transform”, J Opt Soc Am A, 18(8), 1871-1881 (2001) [9] J Schwider, R Burrow, K.E Elssner, J Grzanna, R Spolaczyk, K Merkel, “Digital wave-front measuring interferometry: some systematic error sources”, Appl Opt 22(21), 3421-3432 (1983) [10] P Hariharan, B Oreb, T Eiju, “Digital phase-shifting interferometry: a simple error compensating phase calculation algorithm”, Appl Opt 26(13), 2504-2505 (1987) [11] M Servin, J.A Quiroga, J.L Marroquin, ”General n-dimensional quadrature transform and its application to interferogram demodulation”, J Opt Soc Am A, 20(5), 925-934, 2003 [12] K.G Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry”, J Opt Soc Am A 13(4), 832-843 (1996) [13] K Patorski, A Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis”, Opt Eng 45(8), 085602, (2006) Index Abetkovskaia, 551 Adamczyk, 27, 37, 47, 62, 161 Alexandrescu, 516 Andrei, 531 Anwar, 556 Bacescu, D., 136, 516 Bacescu, D.M., 136 Balemi, 355 Bałasz, 273 Baranouski, 679 Barczyk, 406 Baszak, 591 Bauma, 438 Bernat, 431 Besnea, 516 Biało, 243, 370, 470 Bieńkowski, 616 Bodnicki, 77 Bogatu, 136, 288, 391, 516 Bohm, 458 Bojko, 381 Bratek, 561 Brezina, 156 Březina, 185, 195 Brocki, 87, 116 Buczyński, 401, 406 Bukat, 313, 340 Burhanudin, 500 Bzymek, 27, 258 Caballero, 156, 195 Cernica, 288, 391 Chikunov, 541 Chizhik, 541, 551 Delobelle, 531 Demianiuk, 308 Denkiewicz, 546 Dobosz, 627 Dovica, 335 Drozd, 293, 298, 313, 340 Duminica, 288 Dwórska, 648 Dymny, 616, 637 Ekwińska, 505, 536 Ekwiński, 505 Fabijański, 16, 141 Fidali, 258, 263 Florian, 195 Gambin, 526 Gheorghiu, 571 Girulska, 313 Golnik, 206 Gorecki, 531 Gorzás, 335 Greger, 421 Grepl, 6, 120, 126, 190, 318 Hadaš, 350 Hartmann, 658 Hirsinger, 531 Hoffmann, 345 Horváth, 278 Houfek, 411 Houška, 107, 151, 185 Huták, 222 Ichiraku, 556 Ikeda, 500 Ionascu, 288, 391, 516 Jabloński, 556, 591, 596, 663, 673 Jakubowska, 360 Janeček, 453 Janiszowski, 323, 475 Jankowska, 57 Januszka, 52 Jarzabek, 541 Jasińska-Choromańska, 211, 233, 401, 406 Jaźwiński, 268 Jezior, 360 Józwik, 531 Just, 396 Kabziński, 401 Kacalak, 375, 431 Keränen, 643v Kipiński, 200, 238 Kisiel, 293, 313 Klapka, 448 Klug, 345 Kluge, 350 Kłoda, 11, 611 Koch, 345 Kocich, 421 Kołodziej, 211 692 Konarski, 243 Korzeniowski, 233 Koržinek, 87, 116 Kościelny, 167 Kowalczyk, 386 Kozacki, 653, 668 Kozánek, 438 Krajewski, 653, 658 Krejci, 190, 576 Krejsa, 107, 151, 416 Křepela, Kretkowski, 663 Krezel, 658 Krężel, 643, 658 Królikowski, 273 Krupa, 531 Kubela, 22 Kucharski, 227 Kuczyński, 475, 616 Kudła, 303 Kujawińska, 227, 637, 643, 653, 658 Kupka, 453 Kurek, 32 Kuznetsova, 541 Lam, 111 Láníček, 222 Lapčík, 222 Lewenstein, 216 Ligowski, 556 Łagoda, 16, 141 Łuczak, 511 Maciejewski, 146 Maga, 67, 72 Majewski, 465, 490 Makuch, 375 Malášek, 426 Malinowski, 365, 480 Manea, 288, 391 Marada, 102 Mayer, 621 Mazůrek, 448, 601 Mąkowski, 596 Meuret, 653 Mężyk, 248 Michałkiewicz, 637 Miecielica, 308 Mikulski, 52 Moczulski, 47, 52 Index Mohr, 658 Moraru, 500 Nagy, 278 Necas, 458 Neugebauer, 345 Neusser, 438 Niemczyk, 227 Nieradko, 531 Novikov, 679 Novotny, 486 Nuryadi, 500, 556 Oiwa, 330 Ondroušek, 151, 185 Ondrůšek, 350 Orzechowski, 673 Ostaszewska, 11, 611 Pakuła, 668 Panaitopol, 136, 516 Panfil, 52, 62 Parriaux, 658 Paszkowski, 370, 443, 470 Patorski, 684 Perończyk, 243 Petrache, 136 Piskur, 283 Pistek, 485 Pochylý, 22 Posdarascu, 571 Pozdnyakov, 571 Pražák, 448, 601 Przystałka, 27, 37, 47, 62 Pustan, 521 Putz, 268 Racek, 67, 72 Rasch, 416 Rizescu, 391 Roncevic, 355 Rymuza, 505, 521, 536, 541, 546 Salach, 606 Sałbut, 616, 637, 643 Sandu, 391 Šeda, 97 Serrano, 156 Sęklewski, 77 Shimodaira, 663 Šika, 438, 458 Sikora, 42 Singule, 1, 350 Index Siroezkin, 551 Sitar, 67, 72 Sitek, 340 Skalski, 370 Šklíba, 453 Sloma, 360 Słowikowski, 561 Smołalski, 82 Sokołowska, 464 Sokołowski, 366, 464, 484 Sorohan, 385 Steinbauer, 432 Stępień, 166 Styk, 684 Suzuki, 657 Svarc, 180 Sveda, 458 Svída, 566 Syfert, 167, 172 Syryczyk, 313 Szewczyk, 586 Szwech, 293, 313 Szykiedans, 253 Śleziak, 131 Ślubowska, 216 Ślubowski, 216 Tabe, 500, 556 693 Tarnowski, 111, 283, 396 Timofiejczuk, 27, 47, 258 Tomasik, 243 Tonchev, 658 Trawiński, 248 Turkowski, 561, 632 Uhl, 381 Urzędniczok, 581 Valasek, 458 Vĕchet, 107, 151, 190, 411 Vlach, 42, 190 Vlachý, 6, 120 Wawrzyniuk, 648 Wielgo, 536 Wierciak, 495 Wildner, 32 Wissmann, 658 Wiśniewski, 443, 470 Wnuk, 323 Wozniak, 621 Wrona, 298 Yen, 156 Yokoi, 500 Zarzycki, 526 Zelenika, 355 Zenevich, 679 Zezula, 6, 120 ... Engineering 126 /2 (20 01) 8 8-1 02 [2] P Waurzyniak, Manufacturing Engineering 133/1 (20 04) 10 7-1 14 [3] M Yamamoto, I Kanno, S Aoki, Proceedings of 30-th Conference on MEMS (20 00) 21 7 -2 22 [4] R Jabłoński,... On micro hole geometry measurement applying polar co-ordinate laser  677 347 a) 333 45 320 b) 13 27 40 40 35 30 307 53 25 20 29 3 67 15 10 28 0 80 26 7 93 25 3 107 24 0 120 22 7 133 21 3 147 20 0 187 160 173 Fig Results of hole measurement after recalculations... plate, short-coherence interferometry, grating interferometry, grazing incidence interferometry and wavelength-scanning interferometry [1, 2] In this paper we present preliminary investigations