Ten years have passed since the publication of the first edition of this classic text in April 2001. Considerable new material amounting to 100 pages has been added in this second edition. Each chapter now contains a Summary section at the end. The new material in Chapter 4 consists of a detailed comparison of Gaussian apodization with a corresponding beam, determination of the optimum value of the Gaussian radius relative to that of the pupil to yield maximum focal-point irradiance, detailed discussion of standard deviation, aberration balancing, and Strehl ratio for primary aberrations, derivation of the aberration-free and defocused OTF, discussion of an aberrated beam yielding higher axial irradiance in a certain defocused region than its aberration-free focal-point value, illustration that aberrated PSFs lose the advantage of Gaussian apodizaton in reducing the secondary maxima of a PSF, and a brief description of the characterization of the width of a multimode beam. In Chapter 5, the effect of random longitudinal defocus on a PSF is included. The coherence length of atmospheric turbulence is calculated for looking both up and down through the atmosphere. Also discussed are the angle of arrival of a light wave propagating through turbulence, and lucky imaging where better-quality short-exposure images are selected, aligned, and added to obtain a high-quality image.

Ten years have passed since the publication of the first edition in April 2001. Many of the typographical errors were corrected in the Second Printing that took place after 3 years in 2004. Only a small amount of new material, approximately 11 pages, was added at that time. It included Appendix B in Chapter 1, Gaussian OTF in Chapter 4, and an extension of the discussion of the short-exposure image in Chapter 5. Additional corrections were made in the e-version of the book in 2009, and the discussion of Zernike circle, annular, and Gauss polynomials was streamlined utilizing an abbreviated notation with emphasis on their orthonormal form. However, a considerable amount of new material amounting to another 88 pages has been added in this Second Edition. Besides correction of some residual typographical errors, a Summary section has been included in Chapters 2, 3, and 5 for consistency with Chapters 1 and 4. Any compound references have been split into single ones. The new material is primarily in Chapters 4 and 5.

In Chapter 4, a Gaussian pupil obtained by apodization is compared with that of a Gaussian beam. The optimum value of the Gaussian radius relative to that of the pupil to yield the maximum focal-point irradiance is derived. The discussion of the standard deviation, aberration balancing, and Strehl ratio for primary aberrations for different values of the ratio of the beam and pupil radii has been expanded. It is shown that the approximate expression for Strehl ratio in terms of the aberration variance is not suitable for very narrow Gaussian beams. The aberration-free OTF has been extended to that of a defocused system. The problem of balancing defocus aberration with spherical aberration or astigmatism is discussed, illustrating that an aberrated beam can yield a higher axial irradiance in a certain defocused region than its aberration-free focal-point value. The PSFs aberrated by spherical aberration are considered to illustrate the loss of advantage of the Gaussian pupil in reducing the secondary maxima when the aberration is present. The characterization of the width of a multimode beam compared to that of a Gaussian beam is discussed briefly.

In Chapter 5, the effect of random transverse image motion on the PSF has been supplanted by a discussion of the effect of random longitudinal defocus. The coherence length of atmospheric turbulence is calculated for the Hufnagel-Valley model of the refractive index structure parameter, for both looking up and down through the atmosphere. The angle of arrival of the light wave propagating through turbulence is discussed for both the Zernike tilt as well as the centroid of the PSF, showing that they are nearly equal. A brief discussion of lucky imaging is also given, where better quality short-exposure images are selected, aligned, and added to obtain a high-quality image.

Virendra N. Mahajan

El Segundo, California

April 2011