The history of achromatic lenses is briefly reviewed. The latest development is the superachromat, which is corrected for four colors. Since the dispersion of glass can be represented by an equation containing four constants, the superachromat is practically corrected for all colors. The application of the superachromatic principle to thick lenses is described and it is shown that a compound lens can be made superachromatic by making each of its separate components superachromatic.

The Design of Superachromatic Lenses

Chapter 1 The retinal image in the human eye

Published papers and reports dealing with data compression, picture properties and models, picture coding and transmission, image enhancement, and human visual information processing are listed.

Bibliography on data compression, picture properties, and picture coding

Against a background of newly emerged security threats, the well-established idea of utilizing submillimeter-wave radiation for personal security screening applications has recently evolved into a promising technology. Possible application scenarios demand sensitive, fast, flexible and high-quality imaging techniques. At present, best results are obtained by passive imaging using cryogenic microbolometers as radiation detectors. Building upon the concept of a passive submillimeter-wave stand-off video camera introduced previously, we present the evolution of this concept into a practical application-ready imaging device. This has been achieved using a variety of measures such as optimizing the detector parameters, improving the scanning mechanism, increasing the sampling speed, and enhancing the image generation software. The camera concept is based on a Cassegrain-type mirror optics, an optomechanical scanner, an array of 20 superconducting transition-edge sensors operated at a temperature of 450 to 650 mK, and a closed-cycle cryogen-free cooling system. The main figures of the system include: a frequency band of 350±40 GHz, an object distance of 7 to 10 m, a circular field of view of 1.05 m diameter, and a spatial resolution in the image center of 2 cm at 8.5 m distance, a noise equivalent temperature difference of 0.1 to 0.4 K, and a maximum frame rate of 10 Hz.

Toward high-sensitivity and high-resolution submillimeter-wave video imaging

Tables are presented giving the MTF of an aberrationless defocused lens with circular aperture for objects illuminated with incoherent monochromatic light. MTF values are given to six decimal places for reduced spatial frequencies νr = 0(0.01)1 and defocusing Δ = 0(0.1)0.4, 0.5(0.5)5, 10(5)50, except that 5/Δ is an upper limit on νr. Here Δ is measured in units of Rayleigh’s 
14λ tolerance on defocusing. The integral of the MTF and (MTF)2 are also given for Δ ≤ 5. The numerical integration was performed by Simpson’s rule over most of the range and by series expansion over the rest. An error analysis is appended. Tables of the line spread function for the focused case are also given.

Tables of the Modulation Transfer Function of a Defocused Perfect Lens

Expressions are derived for the light distribution in the image of a sinusoidal and of a bar (crenelate or “square-wave”) pattern produced by diffraction at a “slit” aperture (straight-sided and infinitely long) and at a circular aperture. In every case, when the pattern has an infinite number of repetitions, the distribution is uniform for the spatial frequency that represents Rayleigh’s limit for two-line sources and a slit aperture; this is thus the absolute objective limit of resolution. In practice, radiation detectors have different thresholds, and, since the rate at which the contrast in the image diminishes as the frequency approaches the limit varies with the type of object pattern and the shape of the diffracting aperture, the measured value of resolving power also varies. A table of the line spread-function for a circular aperture is given.

Imagery of One-Dimensional Patterns

Reasons for the unsuitability of resolving power as a criterion of the performance of an optical or photographic system in general are outlined and the newer concepts of acutance and spread function are introduced. The method of computing the edge trace from the spread function is described. The procedure known as convolution is introduced and exemplified by computing the image of a sinusoidal test object. It is shown that such an image is also sinusoidal and of the same frequency as the object but of different modulation and phase and that the properties of such an image give rise to the concept of sine-wave response.

Methods of Appraising Photographic Systems: Part I—Historical Review

The optical-reduction method of impressing images on emulsion samples for measuring the resolving power of the latter is preferred over the contact-printing method, chiefly for its practical convenience. A description is given of a camera containing a 150-mm f/5 apochromatic telescope objective, which makes 13 exposures to incandescent light on a power-of-two time scale. For materials of high resolving power, another camera is described that accommodates microscope objectives and makes 7 exposures to monochromatic light on any desired time scale. This camera uses distance pieces to position the sample, and the technique of using such pieces is discussed. The methods of making test objects and the precautions required are described.

Photographic Sharpness and Resolving Power. II. The Resolving-Power Cameras in the Kodak Research Laboratory*

The excessive residual aberrations of the ordinary achromatic doublet that had been regularly used to photograph resolving-power test objects on film samples in these Laboratories led to the construction of a special air-spaced apochromatic triplet containing fluorite. So excellent is the correction of the new lens that the Airy disk is white and changing the focus setting to fit the spectral sensitivity of the sample is unnecessary, except when the sensitivity peak is at a wave-length longer than 580 mμ. The improvement in measured resolving power over the values obtained with the former lens is slight for materials of high resolution but is marked for materials whose values are below about 100 lines per millimeter. Curves are presented showing the effect on resolving power of stopping down the new objective, and it is shown that this lens, whose aperture is f/5, is not adequate for materials exceeding 150 lines per millimeter or so, failing simply because of its comparatively low aperture. These results emphasize the dependence of resolving-power values on the aperture and the corrections of the camera lens. The loss in the resolving power of this lens caused by mal-focusing is also compared with that of an anastigmatic photographic objective.

Photographic Sharpness and Resolving PowerI. The Design and Performance of an Apochromatic Resolving-Power Camera Objective*

It was found experimentally that, as the relative aperture of the camera lens increases, the lens being substantially “perfect,” the measured value of the resolving power of an emulsion used with it also increases but eventually attains a maximum and then decreases. It is proposed to call this maximum the “maximum lenticular” resolving power of the emulsion. A hypothetical relation is derived for predicting the measured resolving power of a lens-emulsion combination for the maximum lenticular resolving power of the emulsion and the resolving power of the lens on the Rayleigh criterion, assuming the lens to be “perfect.”

Fred H. Perrin

Papers

Imagery of One-Dimensional Patterns

Methods of Appraising Photographic Systems: Part I—Historical Review

Photographic Sharpness and Resolving Power. II. The Resolving-Power Cameras in the Kodak Research Laboratory*

Photographic Sharpness and Resolving PowerI. The Design and Performance of an Apochromatic Resolving-Power Camera Objective*

Studies in the Resolving Power of Photographic Emulsions. III. The Effect of the Relative Aperture of the Camera Lens on the Measured Value