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(11.41) From (11.41) we notice that the vector [Fd ] on the left-hand side is represented as a linear combination of N independent vectors, which, for the brevity of presentation, we name [E1 ], [E2 En ], respectively. For solutions of unknown terms A1 , AN , a necessary condition is that [Fd ] must lie on the space spanned by the A2 vectors [E1 ], [E2 En ]. Otherwise an exact solution is not possible. For M > N , it is quite possible that [Fd ] lies outside the space of [En ] s. This is pictorially shown in Figure 11.16 for N = 2 and M = 3. The best possible solution in the least squares

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, Automated Interferometic System for Aspheric Surface Testing, Proc SPIE, 680, 71 (1986) Kim C-J, Polynomial Fit of Interferograms, Appl Opt, 21, 4521 (1982) Kim, Shannon, 1987 Kim, C J and RR Shannon, Catalog of Zernike Polynomials , in Applied Optics and Optical Engineering, Vol x, RR Shannon and JC Wyant, Eds Academic Pres, San Diego, 1987 Kinnstaetter K, A W Lohmann, J Schwider, and N Streibl, Accuracy of Phase Shifting Interferometry, Appl Opt, 27, 5082 (1988) Koliopoulos C L, Interferometric Optical Phase Measurement, PhD Dissertation, University Arizona, Tucson, 1981 Koliopoulos C L, Radial Grating Lateral Shear Heterodyne Interferometer, Appl Opt, 19(9), 1523 (1980) Kothiyal M P and C Delisle, Optical Frequency Shifter for Heterodyne Interferometry Using Counterrotating Wave Plates, Opt Lett, 9, 319 (1984) Kothiyal M P and C.

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Delisle, Shearing Interferometer for Phase Shifting Interferometry with Polarization Phase Shifter, 24, 4439 (1985a) Kothiyal M P and C Delisle, Shearing Interferometer for Phase Shifting Interferometry with Polarization Phase Shifter, Appl Opt, 24, 4439 (1985b) Kozlowski, L J, K Vural, V H Johnson, J K Chen, R B Bailey, D Bui, M J Gubala, and J R Teague, 256 256 PACE-1 PV HgCdTe Focal Plane Arrays for Medium and Short Wavelength Infrared Applications, Proc SPIE, 1308, 202 (1990) Kreis T, Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method, JOSA A, 3, 847 (1986) Kuechel M F and W Wiedmann, In-Process Metrology for Large Astronomical Mirrors, Proc SPIE, 1333, 280 (1990) Kuechel M F, Advances in Interferometric Wavefront-Measuring Technology Through the Direct Measuring Interferometry Method, Proc SPIE 1573, 159 (1992a) Kuechel M F, Advanced Interferometry at Carl Zeiss (Summary Only), Proc SPIE, 1720, 452 (1992b).

Kuwamura S and I Yamaguchi, Wavelength Scanning Pro lometry for Real-Time Surface Shape Measurement, Appl Opt, 36, 4473 4482 (1997)..

P.I.P.S. is designed to provide support for standard C programming in a POSIX environment with the dual goals of improving the productivity of existing developers porting software from other platforms and making the Symbian platform more attractive to other developers with C/C++ skills. The P.I.P.S. APIs also enable the addition of a number of extension libraries to the platform, adding support for further standard APIs. The rst of these extension libraries was shipped by Nokia along with the core P.I.P.S. libraries in a package called Open C, very shortly after the initial release of P.I.P.S.

(a) Find a series expansion for K(k). [Hint: Recall (3.80).]

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T * := { t T * | AvailCap(t ) mod L(d) = Mint T* { AvailCap(t ) mod L(d ) } }

0.092 0.099 0.116

(9.25)

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