Extreme Focal Depth in Microscopy Dan McLachlan, Jr. This paper describes and gives some of the results of using a microscope which increases the useful depth of observation of an object in a photograph to many times the focal depth of the lens system being used. The principle of the microscope is that the object is illuminated only on the focal plane while the object is being scanned through that plane. Thus, the out-of-focus parts of the object are always in darkness, and the final photographs show high resolution throughout the depth of scan. The mechanism of scan- ning is somewhat similar to the Gregory-Donaldson method, whereas the mechanism of illumination is sim- ilar to that of the Schmaltz slit. This is the first time that scanning and focal plane illumination have been combined to attain high resolution at great depths. Of course, high-frequency scanning would per- mit direct observation by eye. Almost from the beginning of microscopy, in the days of Kepler and Descartes, the problem of focal depth has plagued us in the use of lenses at high magnification. The purpose of this paper is to describe a method for solving this problem. Although the method and the bulk of discussion are illustrated with radiation in the visible region of the spectrum, it is applicable to infra- red, ultraviolet, electron (mirror or reflection), and ion bombardment microscopes, or the use of any form of radiation where scattering and focusing of radiation are involved. Referring to Fig. 1, we have a schematic representa- tion of a sample S, a lens L, and a photographic plate P. The sample S, as can be seen, has an irregular shape and is mounted on a block M. The lens has a diameter a and a focal length f. In the usual way, the distance p from the lens L to the focal plane FP, and the distance q from the lens L to the plate P are related by the equa- tion, 1 1 1 f = q (1) and the magnification is M = qp, (2) while the resolution on the focal plane FP is h = X/27 sinU. (3) Since the human eye can tolerate a circle of confusion of about 0.0125 cm or 8 lines per mm under the best conditions (according to Needham'), then there is a circle of confusion c which is all that a microscope needs to attain at a given magnification M: The author is with The Ohio State University, Columbus, Ohio. Received 5 January 1964. c= 0.0125/M (4) and this value c is also related to the angle U (see Fig. 1) and to an important quantity Do, the optical focal depth. Since c/Do = a/2p, (5) then we have an equation for the tolerated focal depth Do = 0.025 p/aMT. (6) If a sample were infinitely thin, the sample could be placed on the FP plane of Fig. 1, and the ultimate re- sults predicted by Eq. (3) could be attained. How- ever, for all practical samples, the depth of the sample, heretofore, had to be kept equal to or less than Do ex- pressed in Eq. (5). In metallurgy, this is achieved by polishing the specimens (and fractography and other problems are difficult to study); in biology and histol- ogy, the sample is sliced thin by a microtome or by other means; in the study of suspensoids, such as blood, the liquid is placed between two glass plates and pressed; the mineralogist,at great cost, grinds the specimensun- til they are thin; and so on. But no technique thus far devised has made it possible to take microphoto- graphs of insects, bacteria, extremely small crystals, woven textiles, broken surfaces of metals, or such small objects of fine texture at high magnification in focus for the complete depth of the object. Many persons have, no doubt, thought of im- proving the resolution in depth by scanning the sample through the focal plane by means of a screw G (Fig. 1) in a direction parallel to the axis of the lens (without turning). This procedure does assure that every part of the sample does sometime come into focus on the plate P. However, there are two difficulties encoun- tered in this maneuver. The first difficulty is that each of the out-of-focus points is magnified at a different September 1964/ Vol. 3, No. 9 / APPLIED OPTICS 1009
Transcript
Extreme Focal Depth in Microscopy
Dan McLachlan, Jr.
This paper describes and gives some of the results of using a microscope which increases the useful depthof observation of an object in a photograph to many times the focal depth of the lens system being used.The principle of the microscope is that the object is illuminated only on the focal plane while the objectis being scanned through that plane. Thus, the out-of-focus parts of the object are always in darkness,and the final photographs show high resolution throughout the depth of scan. The mechanism of scan-ning is somewhat similar to the Gregory-Donaldson method, whereas the mechanism of illumination is sim-ilar to that of the Schmaltz slit. This is the first time that scanning and focal plane illumination havebeen combined to attain high resolution at great depths. Of course, high-frequency scanning would per-mit direct observation by eye.
Almost from the beginning of microscopy, in the daysof Kepler and Descartes, the problem of focal depth hasplagued us in the use of lenses at high magnification.The purpose of this paper is to describe a method forsolving this problem. Although the method and thebulk of discussion are illustrated with radiation in thevisible region of the spectrum, it is applicable to infra-red, ultraviolet, electron (mirror or reflection), and ionbombardment microscopes, or the use of any form ofradiation where scattering and focusing of radiation areinvolved.
Referring to Fig. 1, we have a schematic representa-tion of a sample S, a lens L, and a photographic plate P.The sample S, as can be seen, has an irregular shapeand is mounted on a block M. The lens has a diametera and a focal length f. In the usual way, the distance pfrom the lens L to the focal plane FP, and the distanceq from the lens L to the plate P are related by the equa-tion,
1 1 1f = q (1)
and the magnification is
M = qp, (2)
while the resolution on the focal plane FP is
h = X/27 sinU. (3)
Since the human eye can tolerate a circle of confusionof about 0.0125 cm or 8 lines per mm under the bestconditions (according to Needham'), then there is acircle of confusion c which is all that a microscope needsto attain at a given magnification M:
The author is with The Ohio State University, Columbus, Ohio.Received 5 January 1964.
c= 0.0125/M (4)
and this value c is also related to the angle U (see Fig. 1)and to an important quantity Do, the optical focaldepth. Since
c/Do = a/2p, (5)
then we have an equation for the tolerated focal depth
Do = 0.025 p/aMT. (6)
If a sample were infinitely thin, the sample could beplaced on the FP plane of Fig. 1, and the ultimate re-sults predicted by Eq. (3) could be attained. How-ever, for all practical samples, the depth of the sample,heretofore, had to be kept equal to or less than Do ex-pressed in Eq. (5). In metallurgy, this is achieved bypolishing the specimens (and fractography and otherproblems are difficult to study); in biology and histol-ogy, the sample is sliced thin by a microtome or by othermeans; in the study of suspensoids, such as blood, theliquid is placed between two glass plates and pressed;the mineralogist, at great cost, grinds the specimens un-til they are thin; and so on. But no technique thusfar devised has made it possible to take microphoto-graphs of insects, bacteria, extremely small crystals,woven textiles, broken surfaces of metals, or such smallobjects of fine texture at high magnification in focusfor the complete depth of the object.
Many persons have, no doubt, thought of im-proving the resolution in depth by scanning the samplethrough the focal plane by means of a screw G (Fig. 1)in a direction parallel to the axis of the lens (withoutturning). This procedure does assure that every partof the sample does sometime come into focus on theplate P. However, there are two difficulties encoun-tered in this maneuver. The first difficulty is that eachof the out-of-focus points is magnified at a different
Fig. 1. A schematic drawing showing the principles of a deep
focus microscope. Note that the zone of illumination is thinnestwhere it crosses the axis of the lens L.
M, and the background is consequently a record ofconflicts. This was overcome by Gregory and Donald-son2 who synchronously moved the plate with the objectin such a manner as to make the out-of-focus and the in-focus points come into register. Another difficulty(which was almost revealed in stating the first one) isthat the out-of-focus images pile up during the ex-posure (even in the Gregory-Donaldson method) toproduce a milky background.
The method, which we herein describe, corrects thesecond difficulty named by so illuminating the object, sothat any part of the object which is out of focus is in
total darkness; the first difficulty named, therefore,needs no consideration.
In the upper part of Fig. 1, we show a light sourceL' and a slit S' and a lens L'. The light from the slitis passed as a thin zone of light to the mirror-prismM', where it is reflected to the sample perpendicular tothe axis of the lens L, and within the zone DO repre-senting the focal depth. Now if the entire apparatusis held fixed, with the illuminated zone coincident withthe focal zone, while the sample is scanned mechani-cally through a distance (or depth) Dm, we have a ratioof "mechanical depth" to focal depth of
R,11o = Drf/Do.
If, however, we have a slit depth D, (see Fig. 1) that isgreater than DO, the resolution is not ultimate and
RMa = Df/D.
A few remarks should be made here about the scan-ning mechanism and later about the illumination ar-rangement. The symbolic worm G, shown in Fig. 1, isreally the elevating mechanism for the stage of anancient Ernst Wetzlar microscope No. 274703, and theblock M is the traveling stage itself, with some attach-ments for adjusting the sample. The pinion on therack of this elevator has a 6.35-mm diam, so that whenthe microscope is tilted to its horizontal position, thesample moves 0.0055 cm per degree of rotation of thegnarled knob. The knob is attached to an arm ofadjustable length from 5.08 cm to 10.16 cm, so that thesample moves from 0.000055 cm per cm of motion of theend of the arm to 0.00022 cm per cm. The motion of
the arm is actuated by a motor running one revolutionper min with a wire over a cluster of pulleys /4, /2,
'/4, 1/8, and '/16 in. (19.05, 12.7, 6.35, 3.18, 1.59 mm) indiameter. This arrangement facilitates scanning thesample at variable rates from 0.00165 cm per see to0.08 cm per see smoothly, so that a microphotograph canbe taken in one sweep. Thus, we see that this scanningprocess need not be as sophisticated as that of Gregoryand Donaldson. 2
The illuminating system is, in principle, the same asthat devised by Schmaltz3 -5 for measuring differencesin elevation on the surfaces of samples of uneven con-tour. The lens L' like the lens L (which are only sym-bolic in Fig. 1) is really of optical microscope quality,because of the accuracy with which the slit-width Dmust be impinged on the sample. The best slit wecould make was produced by spraying flat black painton a microscope slide and cutting a line in the paintwith a new Gem razor blade. As measured by aBausch & Lomb Filar microscope Ramdsen eyepieceA 12.5, the two best slits were relatively uniform inwidth and were 2.4 X 10-4 cm wide and 1.76 X 10-4
cm wide. With an optical system that reduces thedimensions to one-twentieth, D values ranging downto 1.3 X 10-5 or 0.8 X 10-5 are obtained, and areadequate for magnifications as high as 400 or 500.
Table I shows the useful magnifications which mightbe desired in the first column labled MT, followed incolumns 2, 3, 4, and 5 by the characteristics of the ob-jectives on hand: MO, the power of the objective; f,focal length; NA, the numerical aperture which is sinU; and a/2p, the tangent of U. Me is the power of theeyepiece, and BL the bellows length. Under thesechosen conditions, the depth of focus Do as computedfrom Eq. (6) is shown in column 8. The depth ofmechanical scan DM shown in column 9 is computed incm on the grounds that we wish the depth of view to beequal to the width of the field and that magnificationwill bring this width to 5 in. (12.7 cm) on a 4 X 5-in.(10.16 X 12.7 cm) photographic film
DM = 12 .7 /MT. (7)
Also, we used the approximate equation,6
MT = MoMe(BL)/10. (8)
Figures 2(a), (b), and (c) are shown to demonstratethe working principles of the microscope. A piece ofdendritic bismuth, about 6.3 cm2 and having block-likerecesses in it about 13 mm deep, was mounted 45 tothe axis of a 50-mm lens and about 55 mm from it.Figure 2(a) shows a photograph of this material takenat a magnification of about 2, while it was being uni-formly illuminated by parallel light streaming in atright angles to the axis of the lens. A white line is drawnthrough the general area of best resolution, i.e., thatportion of the sample which is most nearly in focus.The bright points on the sample produce circles of in-creasing diameter as the distance from optimum focusincreases, so that one can almost measure the circles ofconfusion with a ruler. A slit of thickness D of 3 mmwas directed upon that portion of the sample that was
in focus and at right angles again to the axis of the lens;the results are shown in Fig. 2(b). One first noticesthat the out-of-focus areas are in total darkness andthus not recorded, while the areas near the white line arerelatively well resolved. However, close inspection indi-cates that D, is about three times DO. Therefore, theslit depth D, of the illumination was reduced to about1 mm before scanning through DM of about 40 mm toproduce Fig. 2(c), a great improvement over Fig. 2(a).
In order to illustrate further the use of this micro-scope, we show in Fig. 3(a) a picture of a half-grownhousefly taken at a magnification of 30 and with ascanning depth of 2 mm. Note the good resolutionthroughout the entire depth of scan. In Fig. 3(b) is apicture of a portion of a sample of dendritic copper takenat 200X.
There are certain remarks that should be made.First, the illumination is from only one direction inthese illustrations. The samples can be easily illumi-nated from more than one direction by suitably placingsmall mirrors on the stage, oriented so as to reflect thelight across and within the focal zone. On the subjectof lighting we find that for transparent objects likesmall quartz crystals or clear synthetic fibers, lightthat once gets inside the object is "piped" to all partsand emerges most strongly at ends, edges, and corners,thus producing illumination that is out of focus. Tocombat this, such objects should first be aerodized ormirror-finished to make their surfaces opaque beforephotographing. It is almost obvious, once one thinksof it, that the scanning motion through the depth DMneed not necessarily be parallel to the axis of the lens L,but can be at almost any angle whatever, or even anonstraight line. We find, as expected, that these mo-tions produce distortions in the image without impair-ing resolution. Also, by obvious means, stereographicpictures can be taken to give further the illusion ofdepth. Another interesting fact is that, since all partsof the object are equal distances from the lens whilebeing photographed, this method gives isometric pic-tures, not perspective pictures.
A last remark has to do with visibility. What onecan expect to see in a picture from this type of micro-scope is analogous to that seen by a helicopter pilotviewing a mountain terrain by moonlight from highaltitude. Figure 4(a) shows the cross section of animagined mountain range incorporating a dome D in aconventional terrain A and a plateau section B. Figure4(b) shows the directions of the moon's rays, and theheavy lines depict the only parts not left in darkness byshadows. Figure 4(c) shows by arrows the pilot's linesof sight, and the heavy lines depict the only parts of themountains not obstructed from view by other parts.Note that to make this illustration fully analogous toour situation, the lines of sight are perpendicular to themoon's rays. Since visibility depends upon both il-lumination and nonobstruction, there is left only theheavily lined portions shown in Fig. 4(d), which thepilot can possibly expect to see.
One observes that in the plateau section B of Fig. 4,only the tops can be seen. This is exactly the case with
Fig. 2. The principles of the microscope illustrated on a largedendrite of bismuth. (a) A picture of the usual kind; (b) thesame sample illuminated by a beam 3 mm deep, not moving; and (c)illuminated 1 mmn deep and mechanically scanned 40 mm.
(b)
Fig. 3. (a) A housefly at 30X; (b) dendritic copper at 200X.
Fig. 4. (a) An imaginary object in cross section; (b) that portion illuminated shown in heavy lines; (c) that part which is visible asviewed in the direction of the arrows; and (d) the part that is both illuminated and unobstructed.
the dendritic bismuth shown in Fig. 2, since this den-drite happened to grow in a form closely resembling apueblo village and only the roofs could be photographed.The dome D in Fig. 4 is more representative of the house-fly in Fig. 3(a). This suggests that the orientation ofthe object is important.
The author is indebted to the Denver Research In-stitute and The Ohio State University for supportingthis research, and to Herbert D. Adams of the Uni-versity of Denver for assistance in the early investiga-tions. The help of Paul R. Lewis of the Department ofMetallurgical Engineering at The Ohio State Universityis appreciated.
References
1. G. H. Needham, The Practical Use of the Microscope (CharlesC Thomas, Springfield, Ill., 1958), p. 223.
2. R. L. Gregory and P. E. K. Donaldson, Nature 182, 1434(1958).
3. G. Schmaltz, Technesche Oberflashenkunde (Springer, Berlin,1936).
4. E. Menzel, Naturwiss. (38) 14, 332 (1951); Optik 14,151 (1957); J. Opt. Soc. Am. 46, 372 (1956).
5. M. Francon, Progress in Microscopy (Row Peterson, NewYork, 1961), pp. 136-142.
6. Reference 1, p. 421.
Books for review should be submitted to the Managing Editor,APPLIED OPTICS, 115516th St., N.W., Washington 6, D.C.
Introduction to Dynamic Morphology. By EDMUND MAYER.
Academic, New York, 1963. 545 pp. $16.00.
Dr. Mayer is an extraordinary man who has written an unusualbook, based on a full lifetime of study. He was born and edu-cated in Berlin, served in the German Medical Corps duringWorld War I, and specialized in clinical and experimental pa-thology in Europe and the Near East. He became a citizen of theU.S. and served medical research for two years at Harvard and(since 1943) at the American Cyanamid Company. From thebeginning of his studies, Mayer was skillful in both macroscopicaland microscopical procedures. His interpretations bridge thetwo kinds of results, and he illustrates clearly either by photo-graphy or by drawing. With these skills he has taught dynamicmorphology for a long time. His book expresses his uniquephilosophy at the apex of its development.
Dr. Mayer intends to reach physicists, chemists, biochemists,statisticians, and all scientists who need an understanding ofmorphology. In his Introduction he cites the example ofphysicists who are occupied with ionizing radiation and are facedwith biological effects such as leukemia and mutations. He dealswith the problems of terminology, three-dimensional interpreta-tions, and the custom of presenting pathological morphologywithout presenting or reviewing the normal morphology. Hethen puts himself in the place of the physical scientist and con-nects results with procedures. He also takes up the tasks ofdynamic interpretation of static pictures. He goes beyond
Frey-Wyssling's concept in his book Submicroscopic Morphologyof Protoplasm and Its Derivatives (2nd English ed., Elsevier, NewYork, 1953), a book familiar to industrial microscopists. Mayerdefines and defends dynamic morphology, which deals withvisible biological structures, their time-associated changes, andtheir relations to functions. The term visible refers to per-ception by the unaided and aided eye. Contrast is increased bydifferential staining or phase contrast microscopy. Fluorescentscreens and photographic emulsions enable the use of ultra-violet light, x rays, and electron beams. Mayer uses a physicalmodel to illustrate the usefulness and limitations of optical pro-cedures and the change from randomness to order. He differen-tiates functional from vestigial and ornamental structures andcompares the three kinds in organisms with those in machines.
Part III on procedures, interpretations, and the problems ofpresentation is especially interesting to the optical physicist andto the microscopist. Mayer considers studies for live and for deadmaterial. For live material he includes the use of x rays, fluores-cence microscopy, micrurgy, and surgical exposure of inner organs.For dead material he emphasizes the need for continuity betweenmacro- and microscopical procedures by use of low powers ofmagnification. He also considers that visibility depends on bothresolution and contrast. He critically reviews some, but by nomeans all, of the important books to help one select microscopicalcondensers, objectives, and eyepieces for visual as well as photo-micrographic work. Relatively, his discussions of sampling,fixing, embedding, sectioning, staining, and mounting specimensare extensive. Considering the recent increase in the uses ofelectron microscopical techniques in the field, a greater propor-tion of space could have been devoted to electron microscopicalresults.
In Part IV, "Elementary General Structures", the discussion offibers may be of interest to the readers of Applied Optics. In
Part V, the first chapter, "Principles of Classification in DifferentAreas of Science", touches upon problems which are encounteredboth in physical and in biological sciences.
Mayer has written clearly and carefully but not always in thelanguage preferred by the physical scientists whom he intends toreach. In general, however, the author does fulfill the purposeswhich he set for himself.
T. G. RocHow
Lecture Demonstrations in Physics. Edited by HOWARD A.
ROBINSON. Translated from the Russian by KIRA V. ROBINSON
and HOWARD A. ROBINSON. 35-mm microfilm. AmericanInstitute of Physics, New York, 1963. $5.00.
This book of lecture demonstrations is a condensation of theoriginal eight volumes edited by A. B. Mlodzeevskii of the M. V.
Lomonosov State University in Moscow and published over theyears 1949 to 1954. Chapter IX, Optics, of the translation (1963)
contains some 112 demonstrations (79 pages). Only the older
aspects of classical optics are treated, and the emphasis is on
optical principles to the unfortunate exclusion of instrumentaloptics. Within these limitations there is good material whichcould profitably be used to supplement the body of lecturedemonstration information presently available in this country.
The first three sections contain 29 demonstrations on ray opticswhich, for the most part, are rather similar to those described inSutton's Demonstration Experiments in Physics (McGraw-Hill,1938). An unusual and significant one in this group is No. C12
Projection in a Dark Field (Striation Method), in which the localdensity changes produced by dissolving sugar or hypo crystals inwater are made dramatically apparent on the screen.
Two sections on interference and diffraction (18 demonstra-tions) include several noteworthy experiments. One titledShifting of Fringes with Temperature (No. D3) illustrates theprinciple underlying the interferometric method of studying airflow patterns in wind tunnels. Although the principles of No.D10 Interference Accompanying Reflection from Parallel Planesare described in Wood's Physical Optics (3rd ed., Macmillan,1934), the Russian manual goes on to add information on how to
grow suitable KC103 crystals needed for the demonstration.Section F on Light Emission and Absorption describes 21
demonstrations including a simplified but dangerous version ofWood's classic experiment on the anomalous dispersion of sodiumvapor. In this modified version the sodium is to be melted andvaporized in an iron spoon held in a gas flame. Eight demon-
strations on luminescence are included. A particularly interest-ing one in this group is No. F19 Chemiluminescence in which a
mixture of pyrogallol, formaldehyde, potassium carbonate, andhydrogen peroxide produce the luminescence. Two others ofinterest are No. F16 Phosphorescence and Triboluminescence andNo. F18 Thermoluminescence.
Five sections on polarized light, crystal optics, and anisotropicmedia contain the remaining 44 demonstrations. Among themore uncommon of these is No. H9 Spherulites in which radial
structured crystals such as barium chloride, benzoin, and betolare viewed under microscopic projection with polarized light.Number 14 Dispersion of Optical Axes is especially interesting;plates of biaxial apophyllite crystals cut perpendicular to theacute bisector show the crystal to be positive in red light andnegative in blue. The next demonstration, No. I5 Optical Axisas a Function of Temperature, points up a curious property of
gypsum: the two optical axes gradually merge as the temperatureis increased and, after merging, again separate in a differentdirection as the temperature is still further increased. A specialcolloidal preparation of ammonium vanadate made up severaldays in advance is used to demonstrate Flow Birefringence (No.J6).
In summary, it must be repeated that this otherwise interestingmanual suffers from twin faults: (1) it is out of date, and (2)it is not sufficiently comprehensive. In making the first criti-cism one must, of course, take into consideration the originaldate of publication, but even after due allowance has been made
it still remains evident that there is a surprising lack of demon-strations illustrating recent progress in optics. Most of theexperiments could well have been written in the early 1940's orbefore. The only reference in the bibliography of this chapter is
Wood's Physical Optics. The manual, therefore, does little tocounter the false impression of many people that optics, particu-larly geometric optics, is pass6. For example, there are no dem-onstrations of such devices as aspheric lenses or mirrors, corner
reflectors, Fresnel lenses, or moir6 fringes. The wave optics
sections should include demonstrations of multiple-beam inter-ference and channeled spectra (FeCO bands). Pohl's elegant andhandsome demonstration of interference with a mica sheet isregrettably missing. (All of the above mentioned antedate 1949.)In addition, one would surely expect a large group of optics dem-onstrations to include at least a few on telescopes, microscopes,spectroscopic systems, and interferometers, but (except for No.E6 Resolving Power of a Microscope) they are conspicuouslyabsent as are also demonstrations on physiological optics.This book, in short, does contain useful and interesting supple-mentary material, but could not be regarded as a replacementfor such books as Sutton's.
C. HARVEY PALMER, JR.
Optical Processing of Information. Edited by DONALD K.POLLOCK, CHARLES J. KOESTER, and JAMES T. TIPPETT. Spartan,Baltimore, Md. 286 pp. $7.50.
In many ways it is strange that optical radiation has not beenthe basis of a technology in computing-today magnetics is kingof all computing technology. This book is a collection of papersgiven at a symposium October 1962 in Washington, D. C., co-
sponsored by the Office of Naval Research and the AmericanOptical Company. Apart from this symposium, many scientistsand engineers have seriously considered optical phenomena forcomputing purposes. The fundamental difficulty lies in thetransducer converting optical frequencies, or photons, back tooptical frequencies. In magnetics it is easy to go from the de-tection of a magnetic field, through an electric field, back to themagnetic field. The magnetic reading head is small and cheap.Nevertheless, the field of a magnetic read-head can never bemade extremely small, and therein remains the appeal of optics.Photons are cheap, uniform, and small. Thus it is importantthat periodic reviews of the possibilities of optics in computingbe made. Can we be sure when the men from Mars (or a-Centuri) arrive they will bring with them cores, tapes, and drumsand not some other electromechanical phenomenon?
During World War II, the electrical engineers, especially inradar, learned a great deal from optics, and classical concepts ofdiffraction patterns of optics became refreshing points of view inanalyzing and designing radar equipment. Now the shoe is onthe other foot, and optics has much to learn from the electricalengineer, e.g., the use of Fourier transforms, transmittance func-tions, and compensating networks. Marechal's chapter on opti-cal filtering is an example-true, the implementation in opticaldata processing can be different from radar data processing.
The technique of radar and optics must necessarily be differentbecause of the frequency or wavelength of the two radiations tobe processed, although Teagher in a more general introductorychapter points out the overlap may be upon us. The nanosecondswitching time of electronics is the foot-second of optical systems.The nonlinear properties (i.e., refractive index) of some crystals
