By Virendra N. Mahajan
ISBN-10: 081948699X
ISBN-13: 9780819486998
Ten years have handed because the ebook of the 1st version of this vintage textual content in April 2001. significant new fabric amounting to a hundred pages has been extra during this moment variation. every one bankruptcy now features a precis part on the finish. the hot fabric in bankruptcy four comprises a close comparability of Gaussian apodization with a corresponding beam, decision of the optimal worth of the Gaussian radius relative to that of the scholar to yield greatest focal-point irradiance, distinct dialogue of normal deviation, aberration balancing, and Strehl ratio for fundamental aberrations, derivation of the aberration-free and defocused OTF, dialogue of an aberrated beam yielding larger axial irradiance in a undeniable defocused area than its aberration-free focal-point worth, representation that aberrated PSFs lose the benefit of Gaussian apodizaton in decreasing the secondary maxima of a PSF, and a quick description of the characterization of the width of a multimode beam. In bankruptcy five, the influence of random longitudinal defocus on a PSF is incorporated. The coherence size of atmospheric turbulence is calculated for having a look either up and down in the course of the surroundings. additionally mentioned are the attitude of arrival of a gentle wave propagating via turbulence, and fortunate imaging the place better-quality short-exposure photographs are chosen, aligned, and additional to procure a fantastic photo.
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Additional info for Optical Imaging and Aberrations, Part II. Wave Diffraction Optics
Example text
1-86) c For a radially symmetric image, Eq. (1-86) reduces to rc Pi (rc ) = 2 / 0 Ii (ri ) ri dri . (1-87) 0 Or, substituting Eq. (1-85) into Eq. (1-87) and noting that11 z0 0 J0 (az ) z dz = ( z0 a) J1 (az0 ) , (1-88) 0 u where J1 ( ) is a first-order Bessel function of the first kind, we obtain Pi (rc ) = 2 / rc Pex 0 o (vi ) J1 (2 / vi rc ) dvi . (1-89) Equation (1-89) gives the encircled power of the image in terms of the radially symmetric OTF of the system. 2 Physical Significance of OTF To understand the physical significance of the OTF defined by Eq.
Evidently, it r depends on the location ro of the object element. We now introduce a relative pupil r r function G rp ; ro ; zi that represents the complex amplitude per unit amplitude of the object element. The two pupil functions are related to each other according to r ( (r r P rp ; ro ; zi ) ) r (r r = U ( ro ) G rp ; ro ; zi ) , r (1-53) r where U ( ro ) is the amplitude at a point ro . It should be evident that the two pupil r functions have identical dependence on rp . Substituting Eq. (1-53) into Eq.
2 Fresnel and Fraunhofer Approximations For large values of z, kl >> 1, l ~ z (so that the obliquity factor z l , representing the cosine of the angle P vP makes with the z axis, may be assumed to be unity) except in the exponent where we retain additional terms according to Eq. (1-21b) to within a fraction of a wavelength (since they are multiplied by k). Hence, Eq. (1-20) may be written r U (r ; z) = £ £ ikr v 2 ¥ r £ 2 /i r r ¥ r > k r < r v max 8 ( Fresnel) , (1-22a) and r U (r ; z) = £ £ 2 /i r r ¥ r r2 ¥ G r > krmax v 2 2 ( Fraunhofer ) .