Spie Press BookAn Introduction to Microdensitometry
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- CHAPTER 1. DENSITOMETRY
- 1.1 Optical density measurements
- 1.2 Practical density measurements:a first look
- 1.3 Density standards approach
- 1.4 Calibration of densitometers
- 1.5 Why calibrate?
- 1.6 Summary
- CHAPTER 2. IDEAL FIRST-ORDER MICRODENSITOMETER CONFIGURATION
- 2.1 Microdensity
- 2.2 General microdensitometer system requirements
- 2.3 Microdensitometer optics
- 2.4 Microdensitometer apertures
- 2.5 Light source and detection
- 2.6 The platen
- 2.7 Scanning
- 2.8 The microdensitometer model
- 2.9 The classical microdensitometer
- CHAPTER 3. SOME PREPARATORY MATHEMATICS AND PHYSICAL OPTICS
- 3.1 The Fourier transformation
- 3.2 The delta function
- 3.3 Complex conjugates
- 3.4 Modern optical imaging
- 3.5 A lens for the far field
- 3.6 Imagery with a lens
- 3.7 Linear optical systems
- 3.8 The cylindrical lens
- 3.9 The circular lens
- 3.10 Coherence considerations
- 3.11 Solution of the wave equation
- 3.12 The quasi-monochromatic approximation
- 3.13 The propagation of mutual intensity
- 3.14 Incoherent source
- 3.15 The van Cittert-Zernike theorem
- 3.16 System characterization
- 3.17 Coherent limit
- 3.18 Additional topics
- CHAPTER 4. SCALAR MICRODENSITOMETER PERFORMANCE ANALYSIS
- 4.1 Microdensitometer coherence measurements
- 4.2 Preliminary system specifications
- 4.3 Analytical assumptions and further specifications
- 4.4 Microdensitometer imaging
- 4.5 Coherence extremes
- 4.6 A generalized mutual intensity
- 4.7 Sampling and the sampling aperture
- 4.8 Some necessary parameters
- 4.9 Linear microdensitometer performance
- 4.10 Effective incoherence
- 4.11 Flare light
- 4.12 Aperture misalignment
- 4.13 Sampling
- 4.14 The linear microdensitometer
- 4.15 Operations
- CHAPTER 5. MEASUREMENT AND COMPUTATION OF EFFECTIVE APERTURE
- 5.1 Microdensitometer optics and apertures
- 5.2 The need to know effective aperture
- 5.3 Measurement of influx and efflux magnifications
- 5.4 Magnification measurement protocol
- 5.5 Constructing a magnification table
- 5.6 Hard and soft apertures
- 5.7 Calculating cutoff frequencies
- 5.8 Calculating effective apertures: a protocol
- 5.9 Application to the model microdensitometer
- 5.10 The remaining issues
- CHAPTER 6. THE CONFIGURATION OF A MICRODENSITOMETER
- 6.1 Frequencies of importance
- 6.2 The frequency of interest
- 6.3 Maximum probable specimen frequency revisited
- 6.4 Configuration
- 6.5 The reevaluation of effective incoherence
- 6.6 Miscellaneous concerns
- 6.7 Two configuration examples
- 6.8 The analysis of configurations
- 6.9 General configuration concerns
- CHAPTER 7. THE CALIBRATION OF MICRODENSITOMETERS
- 7.1 General aspects of calibration
- 7.2 Unconventional, bootstrap, microdensitometer
- CHAPTER 7 (Continued)
- 7.3 Bootstrap critique
- 7.4 Bootstrap protocol
- 7.5 Calibration miscellany
- CHAPTER 8. ASPECTS OF PRACTICAL OPERATION
- 8.1 Installation
- 8.2 Maintenance
- 8.3 Operational and usage miscellany
- 8.4 Microdensitometer health checks
- APPENDIX A COMPUTER PROGRAMS
- A.1 FILRED.BAS
- A.2 DENTAB.BAS
- A.3 FIXFIL.BAS
- A.4 EFFAPT.BAS
- A.5 TI-60 program, no name
- A.6 APPROX.BAS
- A.7 NEWTON.BAS
- APPENDIX B LINEARITY CONDITIONS FOR CASES I AND II
Microdensitometry, in it's simplest sense, is the measurement of optical density in a vanishingly small portion of a specimen. The portion in question is much too small to measure on a densitometer, which has circular sampling apertures with diameters no smaller than 2 or 3 millimeters. In addition to this size restriction, there is ordinarily a requirement to look at a number of contiguous specimen areas, and this requires a scanning capability. Add to this the requirements for positional accuracy, photometric fidelity and rapid throughput. The essential equipment to carry out microdensitometric measurements, even within this shortened list, offers an awesome challenge to the designers and builders of such instruments. Yet, over the years, such instruments have been produced and used. As the demand for more rapid turnaround, higher resolution and photometric stability over long scan-times has increased, the instruments have grown in complexity and cost. Some of the microdensitometers that were built and marketed have been excellent, fulfilling the promise of the designers, more or less, and meeting most of the requirements of the users.
The early instruments were slow, generally bulky and noisy, but had adequate resolution for the tasks they carried out. The instrumentation improved with development and the growth of several areas of technology (photomultipliers, interferometric distance measurement, analog-to-digital and log circuitry, to name a few) allowed the instruments to be made smaller, quieter, faster, more accurate and much more versatile.
Despite the differences in the instrumentation from manufacturer to manufacturer, the underlying principles of operation and usage were identical. Yet the understanding and exploitation of the full instrument capability did not mirror the quality of the instrumentation in the earlier years. Microdensitometry, for a long period of time has been a black art--not a science. This stems from several factors, one of the most important of which was that the coherence of the illumination and the nuances of physical optics on instrument operation were not fully appreciated. The manufacturer commonly provided manuals for adjustment and routine operation of the microdensitometer, but the principles of microdensitometry were neglected. It was left for the instrument user to "fill in the blanks," and too often the user had neither the time nor the knowledge to answer the questions. It is fair to say that many did not even know there were questions.
Beginning in the early 1970's, the theory of partial coherence together with the concepts of physical optics was applied to the analysis of microdensitometer performance. This began an avalanche of papers on the subject, and brought the use of the instrument to a significantly higher level of understanding. The growth of knowledge in this field is fascinating to watch. It has recently been documented(1) by the author.
What is still lacking is a primer on microdensitometry which brings all the knowledge developed over the past forty years into a single source. This book is aimed at providing such a text. It concentrates on the basic aspects of microdensitometry in terms of modern optical theory, while providing practical details for the prospective users of these instruments. This should allow them to utilize the full potential of which their particular microdensitometers are capable.
While there are many possible variations of the microdensitometer, only one type will be covered in this book: the so-called classical microdensitometer. This instrument has a scanning table upon which the specimen is located, an optical system which illuminates the specimen and an optical system which scans the specimen and images it onto an aperture. The light flux passes through this aperture to a detector, where a signal is generated. From this signal comes a value of optical density.
What characterizes this type of instrument is flexibility. Adjustments in apertures, optics and scan parameters are independent of one another. It is called classical because all other densitometers are variations of it, and knowledge of this type can be applied to all the others. Its useful and effective operation requires decisions on the part of the microdensitometrist at nearly every step: carefree microdensitometry cannot be carried out on the classical instrument. One of the purposes of this text is to enable the microdensitometrist to make these decisions in a logical, informed manner, so that the instrument can reach its full potential. The aim is to elevate microdensitometry to a science and take its operation out of the realms of art and luck.
The book begins with a brief discussion of densitometry, in Chapt. 1. The proper adjustment and calibration of densitometers emphasizes their importance in the laboratory as an adjunct of the microdensitometry carried out there. Because much of the specimen material examined on the microdensitometer is photographic in nature, the effects of scattering on the measurements are treated.
In Chapt. 2, the ideal first-order microdensitometer is described (configured). Here the emphasis is on components, some aspects of hardware, first-order imaging, apertures, scanning, glass platens and detection. Performance is discussed only in general terms. The chapter's purpose is to develop a model instrument that will serve as the basis for subsequent analysis.
Chapter 3 provides the basic mathematical framework for performance analysis and gives the reader the essential ideas from physical optics and the theory of partial coherence to help understand the nonlinear problems with the microdensitometer.
Chapter 4 analyzes the first-order configuration developed in Chapt. 2, and develops the basis for what can be accomplished in microdensitometry. Here the ideas central to the decisions the microdensitometrist must make are developed and explained.
Chapter 5 discusses the problem of specifying the effective apertures; i.e., those apertures that are produced by the imaging of real, physical apertures with optics whose magnifications are not those printed on the lens barrels. Methods of magnification measurement are discussed and the calculation of tables based on them are treated.
Chapter 6 considers the problems of configuration for the instrument to accomplish a specific task: the decisions that must be made to choose optics, apertures and scanning parameters. A protocol for a logical method of selection is presented. An alternate configuration for some microdensitomters is also discussed, as an aid to the practical operation of some instruments.
Chapter 7 discusses the need for and the problems attendant to calibration, suggesting a protocol for logical use. The problem of calibration for specimens about whose physical characteristics nothing is (apparently) known is treated.
Chapter 8 considers some aspects of the practical operation of microdensitometers, including such things as cleanliness, temperature control, vibration, routine maintenance, operational quality checks and noise.
A brief Epilogue is added to review some of the reasons for excluding some topics and discussions centered about specific instrumentation.
To aid the reader in using some of the procedures outlined in this book, Appendix A lists several useful computer programs, in the BASIC language. Appendix B contains the analysis of two microdensitometer cases, detailing the transfer functions and linearity specifications.
Richard E. Swing