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The spectral density functions g(k) of the surface roughness for polished optical surfaces of CaF2, MgF2, and LiF are computed from autocovariance functions, which in turn have been determined from surface profiles obtained by using a microdensitometer analysis of electron micrographs of shadowed surface replicas. The fast-Fourier-transform algorithm and a smoothing procedure have been used to determine the g(k) estimates. It is shown that g(k) is not a Gaussian function throughout, as is usually assumed. Spectral density functions gS′(k) of the surface slopes are also computed, and it is shown that results obtained are consistent with those deduced from g(k). Limitations of our method at low spatial frequency are discussed. An analytical model for g(k) is investigated that should be useful in performing theoretical calculations on scattering problems.

Modulation transfer functions (MTF’s) of high-resolution plates Agfa–Gevaert Scientia 8E70, 8E75, 8E75B, and 10E75 have been determined. A strong influence of the development conditions was found and studied. Observations and models given in the literature on adjacency effects at low spatial frequencies were extended and verified for spatial frequencies up to 1500 cycles/mm. This was possible by the use of a new type of microdensitometer (MSSM) and because the optical MTF of these plates is close to 1. By use of very weak developers, an apparent increase of the MTF by factors up to 2 could be achieved. Because this enhancement occurred only in connection with very low γ, there is no gain of contrast in applications to microreproduction. The diffraction efficiency of holograms was not improved, but exposure latitude was increased. Development effects may alter reconstructed wavefields, and spatial filters may deviate considerably from their designs, especially when low-γ development is used to obtain wide latitude.

An analysis is conducted to determine the effect of random microdensitometer positioning errors on the computed Fourier transform (FT) of measured data. Three statistical measures of the FT are derived: the first two moments and the mean-square error (MSE). Results show that the expected FT is multiplied by the conjugate of the characteristic function of the position errors, whereas the variance and the MSE are multiplied by linear combinations of the same function. Working relationships are developed for both the continuous and discrete cases. The continuous errors were Gaussian and uniformly distributed. A simple model of a counter was used to develop expressions for the discrete case. These simple equations relate the error probability density function, or counter parameters to the relative root-mean-square error of the measured FT. An example drawn from reflection microdensitometry suggests that continuous position error tolerances should be about the order of 0.5 μm, with counter failure probabilities less than 9 × 10−9, for a 10% relative rms error in the FT.

We reconstruct the micrograph images from surface profiles previously obtained1 by using microdensitometer analysis of electron micrographs of surface replicas. These micrograph images compare favorably with the original images.

Autocovariance functions (ACF’s) G(x) for polished optical surfaces of CaF2, MgF2, and LiF are deduced from surface profiles determined by using microdensitometer analysis of micrographs of surface-shadowed carbon replicas. The different estimators allowing the ACF computation from its standard definition are reviewed, and their values are compared. ACF’s are also computed by using the fast-Fourier-transform algorithm. Results of both computations are in good agreement. It is shown that initial portions of ACF’s have a reasonable Gaussian form. The rms roughness height δ and the autocovariance length σ are deduced for each surface. The ACF’s of the surface slopes Gs′(x) are also computed, and it is shown that results obtained are consistent with results deduced from ACF’s for surface profiles. In particular, the standard relation between the second derivative of G(x) and Gs′(x) is reasonably verified. Finally, the exponential ACF model is discussed, and it is shown that this model would not be suitable to describe the initial portions of the ACF’s for the polished optical surfaces that we have studied.

A new method for studying surface roughness is presented that uses a microdensitometer to analyze electron micrographs of shadowed surface replicas. First we give a preliminary description of the replication technique and the microdensitometer analysis. Then we proceed to show that the micrograph density (or transmittance) is approximately proportional to the slope of the surface elements, which enables us to determine the surface profile by integration of the microdensitometer data. Bidimensional and monodimensional median-filtering algorithms are used in the data reduction, and their validity is analyzed. With the help of a computer program that plots a perspective view of rough surfaces, we find that a close approach to the real profiles is obtained. This shows that our method may have other important applications in addition to the study of alterable metallic surfaces.

An inverse densitometric circuit is described which employs the technique of voltage-transfer curve translation to provide a direct linear measure to photographic-energy profiles. An antilog D scale (reciprocal-transmittance scale) linear to ±0.05 antilog D units over a basic antilog D range of 12 is obtained. Neutral-density filters are used to compound the basic sensitivity increment and obtain a total light-level range in excess of 1 to 103. An optical system is described which provides an instrument resolving power of 500 lines/mm.

An account is given of a simple system for producing a sinusoidal exposure distribution in time and space. A “scanning integrator” is used to scan square-topped periodic test objects, thereby presenting the desired exposure distribution to the lens system under test. The effects of various geometrical shapes of the entrance aperture of the scanning integrator on the exposure distribution are investigated. By such a direct scan, sine waves of opacity result on the recording film, which may then be employed for producing sinusoidal transmittance waves by a printing method. Direct sine waves of transmittance are also produced using a nonuniform Ronchi ruling. The simple setup used for this investigation is described, and the microdensitometer traces show that high quality sine wave test objects are obtainable.

In this paper, we consider how much coherence is admissible without affecting the linearity of a microdensitometer. Conditions required for linear operation are presented and discussed. We investigate the strength of these conditions by using differences between the shape of high-contrast- and low-contrast-edge images. The normalized image irradiance is calculated, based upon the theory of partially coherent image formation assuming diffraction-limited optics. Our results show that the numerical aperture of the influx optics must be greater than the numerical aperture of the efflux optics. Higher detail content of the sample requires increased overfilling of the efflux optics. In addition, the coherence interval at the source aperture (or preslit) must be equal to or less than the resolution limit of the microdensitometer when both distances are referred to the scale of the sample plane. Greater incoherence is required as the sample-detail content increases. These results are equally applicable to color or conventional microdensitometry.

The special techniques required to measure the photographic transfer functions defined in Part I are described, and detailed methods of computation are given. A photographic procedure for separating isotropic optical losses into lens and film components is discussed; results of this method are compared with data obtained by different methods at other laboratories. Illustrative measurements of both optical and chemical transfer functions are presented for several different emulsions and processing techniques. These data are consistent with the model proposed in Part I and with microdensitometer traces of “knife-edge” exposures. It is indicated that the term “adjacency effects” should be abandoned in favor of the more general formulations used here.

The effect of employing coherent illumination (such as a laser source in scanning optical systems) upon image content is investigated with particular reference to the microdensitometer system. The method of investigation involves the application of coherence theory to the imaging process in systems where the small-angle approximations can be made and the optics of the system are diffraction limited. The output of the system is determined for a sharp-edged object as the area illuminated in the object plane or the width of the illuminating slit is varied. A system configuration is found in which the edge image does not exhibit the usual ringing or diffraction fringes associated with coherent illumination.

In Part I four methods are described for measuring the refractive index of strongly absorbing liquids. The first two of these depend upon determination of the critical angle of reflection of monochromatic light at a glass-liquid interface. In the third, white light was reflected at angles near the critical angle and was then allowed to enter a spectrograph. Microdensitometer records were made of the resulting spectrograms. Peaks in the record correspond to maxima of the refractive index. In the fourth method the transmitted light was examined visually in a spectroscope. In Part II these methods have been applied to a saturated aqueous solution of potassium permanganate. As a result a dispersion curve was found with a strong anomaly centering about 5473A and in addition a series of minor anomalies corresponding to the banded structure of the absorption spectrum. It is concluded that the band at 5473A is that caused by the fundamental frequency of an electronic transition in the manganese atom.