Contains a report on a research project.National Institutes of Health (Grant NB-01865-05 and Grant MH-04737-03)Bell Telephone Laboratories, IncorporatedNational Science Foundation (Grant G-16526)National Aeronautics and Space Administration (Grant NsG-496)United States Air Force, Aeronautical Systems Division (Contract AF33(616)-7783)Teagle Foundation, IncorporatedNational Science Foundation (Grant G-16526

Howland, Bradford H.

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XVII. NEUROPHYSIOLOGYW. S. McCulloch R. C. Gesteland Diane MajorM. A. Arbib W. L. Kilmer L. M. MendellF. S. Axelrod K. Kornacker W. H. PittsP. O. Bishop W. J. Lennon J. A. RojasM. Blum J. Y. Lettvin A. TaubJ. E. Brown P. D. WallA. NOVEL OPTICAL SYSTEM FOR COUNTING DROPLETS IN SUSPENSIONIn the course of our experiments with reflexive optical systems, we have developeda method for illuminating transparent droplets in suspension (or bubbles in solution)which may have application to drop-size measurement (disdrometry), or to fluid-flowvisualization. More specifically, this new method permits us to define a plane of illu-mination in a three-dimensional space with greater accuracy than is permitted by con-ventional slit-illumination methods. Droplets crossing this plane of illumination willemit a pulse of light indicative of the size of the drop. The resultant improvement inspacial resolution should permit higher counting rates and/or discrimination of finerdroplets than heretofore.The principles of operation are explained with reference to Fig. XVII-l. Light fromsource Y passes through polarizer Pl and is reflected downward by a beam-splittingprism B. (The undeflected beam is absorbed by black baffles Z and Z'.) A fraction ofthe downwardly directed polarized beam is intercepted by droplets D 1 , D2, D3, etc.Rays passing through these drops will converge at foci F l, F 2 , F 3 , below the droplets,and will subsequently diverge; the divergent rays will be collected by a wide-aperturelens objective, L. This lens is oriented to have its principal focal plane at XX', andconjugate focus at infinity.Rays that pass through the lens are returned in the same direction by a triple mirroror corner reflector, T, located immediately below the lens. A half-wave plate, H, semi-circular in shape so as to intercept each ray once, either before or after passing throughthe corner reflector, rotates the plane of polarization of the returning rays by 90'. Thoserays which are undeflected by droplets are blocked by the absorbing and occluding disc,M, located at the conjugate image of the light source. The rays which were originallydiverted by the droplets after passing twice through the lens will reassemble at the con-jugate focal points, F'1, F', F3, etc. For the purpose of this example, we shall assumethat droplet D 3 is so positioned that its foci F 3 and F' are coincident in plane XX'. Thelight rays which were originally scattered by this droplet will be reassembled so as toreform a beam returning in the direction of the light source (and the observer). LightThis work is supported in part by the Bell Telephone Laboratories, Inc.; TheTeagle Foundation, Inc.; the National Institutes of Health (Grant NB-01865-05 andGrant MH-04737-03); the National Science Foundation (Grant G-16526); and in part bythe U. S. Air Force (Aeronautical Systems Division) under Contract AF33(616)-7783;additional support was received under NASA Grant NsG-496.QPR No. 71 267BEAM - SPLITTINGPRISMLIGHT SOURCEY// D1/1//F/ F X/Fig. XVII-1.-X'(OCCLUDING ANDABSORBING DISC)(LENS)- (HALF -WAVESEMICIRCULARPLATE)(CORNER REFLECTOR)Optical system for droplet illumination.QPR No. 71EYE OFOBSERVER BING268(XVII. NEUROPHYSIOLOGY)scattered by each of the other droplets will reassemble at points either too low or toohigh to be effectively collimated by these same droplets, and their images will be lessapparent to the observer. The rotation of the plane of polarization of the reflected rayspermits us to place a second cross polarizer P 2 in front of the observer with smalladded attenuation; this polarizer will block the direct specular reflection from all ofthe droplets in space S (regardless of position).We see that the cooperative action of this arrangement of elements is such as torender visible only those droplets in the space S which are so positioned to have theirfoci located within narrow limits of the focal plane (or, more generally, surface) of thelens L. To the casual observer, the effect is that which one would associate with anarrow-slit illumination from the edge; one difference being that the droplets light inthe center.A closer examination of the properties of this optical system reveals the followingadditional points. (a) The peak response to a droplet of given size as measured by thetotal light reaching the observer (who might be replaced by a phototube) can be substan-tially independent of the coordinates of the droplet in plane XX'. (b) Suitable choice ofthe size of the occluding stop, M, allows us to eliminate the central portions of the coneof light returned toward each drop by the lens system; thus if the droplet be more thana few radii from the position of maximal illumination, it will be in complete eclipse,and hence invisible to the observer. (c) If a suspension of droplets is propelled atconstant velocity in a normal or oblique direction past the plane of focus, each dropletwill emit a pulse of light of duration and intensity characteristic of its size. (d) Thelimitation of the special resolution of this system along the axial direction is determinedby the diffraction limit of a wide-aperture lens, and is necessarily an improvementover that which it is possible to attain with a comparable working volume with any pos-sible system of slit illumination.Detailed Design Considerations and Results with a Scale ModelThe performance of the optical system described here is largely determined by theproperties of the lens. A particular requirement of special importance is the need forwide aperture, so as to achieve, in effect, minimum depth of field. Wide apertureis usually incompatible with best resolution, which is also a desirable feature if we areto resolve fine droplets. In this special application, however, it is not necessary tocontrol all the primary lens aberration to the degree customary. Table XVII-1, inwhich these seven major aberrations are listed, makes this point. With the relaxationof the need for correction of lateral chromatic aberration and distortion, it may bepossible to effect considerable improvements in the resolution of wide-aperture lenses.If the light source is monochromatic, the freedom from three of the seven usualQPR No. 71 269(XVII. NEUROPHYSIOLOGY)Table XVII-1. Effect of lens aberrations on performance of planar illumination.Aberration Remarks1. Spherical aberration Must be controlled2. Astigmatism Must be controlled3. Coma Effect undetermined4. Distortion Unimportant5. Curvature of field Unimportant for particle-countingapplications6. Lateral chromatic aberration Unimportant7. Axial chromatic aberration Important unless illuminationis monochromaticconstraints would be very likely to permit improvements in resolution and aperture.In order to provide experimental verification of this method of illumination a large-scale model was constructed. The droplets were simulated with glass beads of a sortused for chemical catalysis; they were made of borosilicate glass, and were roughlyspherical.Two different lens objectives were employed for these tests: (a) a 150-mm, f 1.8,Astro-Berlin, "Projektions-Tachar" lens, an extremely high speed four-element longfocal length objective, intended for small and medium format (6 cm X 6 cm) photography.This lens has very good central resolution, and is well color corrected; its chieflimitation for photographic purposes is a pronounced curvature of field. (b) a 7-inchf 2. 5 Aero-Ektar (Eastman Kodak) aerial camera lens, intended for 5 in. X 5 in. format.This lens has also good resolution, is color-corrected and has a very flat field. Theselenses were operated close to their full apertures, limited by the 6-cm diameter of thecorner reflector. The polarizers were Polaroid, and the light source was a micro-scope illuminator. The occluding stop M was black velvet, and absorbing baffles Zand Z' were glossy black surfaces.In Fig. XVII-2 we show the results of illuminating a collection of glass beads,roughly 2 mm in diameter, positioned so as to give maximal light return. (The beadswere sandwiched between discs of optical glass; this and subsequent photographs weretaken with a red filter to reduce the effect of secondary spectrum, or residual axialchromatic aberration.) In Fig. XVII-3 we show the results of inclining this same arrayof beads 30 ° to the plane of focus. Roughly, one row of balls is illuminated here, theothers are dark, save for light scattered by inclusions and imperfections of the beads.In Fig. XVII-4 we show the same display for beads of 1-mm diameter with a lesserQPR No. 71 270Fig. XVII-2. Fig. XVII-3.Fig. XVII-5. Fig. XVII-6 Fig. XVII-7.QPR No. 71Fig. XVII-4.271(XVII. NEUROPHYSIOLOGY)inclination; in Fig. XVII-5 the same picture for 0.5-mm beads. In the latter figure, thecurvature of the illuminated track caused by the field curvature of the 150-mm lens isapparent. In Fig. XVII-6 we show the 0. 5-mm beads slightly inclined (~15*) to the focalplane of the 7-inch Aero-Ektar lens; here, despite the reduced inclination of the beads,the locus of centers of illumination is very nearly straight.In Fig. XVII-7 we show the result with the small (0. 5-mm) beads, the Aero-Ektarlens, and an inclination of 400; in this picture, at most, two rows of balls, separatedin depth 0. 5 mm, are visible simultaneously, In these tests considerably depolarizedlight was returned by the balls, presumably because of inclusions. (There were nopronounced color fringes that are indicative of strains.) It is to be expected that(CORNER REFLECTOR) T(SEMICIRCULAR HALF- HWAVE PLATE)L(LENS)\ jI I "\LIGHT - I PELLICLE (THIN- FILM) BEAM SPLITTERFd II/Fig. XVII-8. One-sided system for observing motions of a layer of bubbles.QPR No. 71 272(XVII. NEUROPHYSIOLOGY)operations with drops or bubbles would produce a display showing better contrast. Theresults presented here, however, should suffice to indicate the feasibility of the method.We anticipate that this method of illumination may have applications in atmosphericstudies, for example, as related to droplet or fog particle-size measurements. A modelfor such purposes could be constructed by using a microscope objective, with the triplemirror replaced by a spherical reflector at the conjugate focal surface. The availabilityof apachromatic wide-aperture objectives should prove advantageous. A second possibleapplication of these methods might be to a problem in fluid-flow visualization. One tech-nique now used for indicating the behavior of flowing fluid is the introduction, by electro-chemical means, of a sheet of tiny hydrogen bubbles generated at a fine platinum-wirecathode. Since the paths of these bubbles will diverge in three dimensions, additionalinformation would be gained if it were possible to illuminate selectively different layersof bubbles in depth. Since the geometry of particular flow situations may be unfavour-able to transverse slit-illumination, and/or the resolution capabilities of slit-illuminationmay be inadequate, the use of the present scheme could prove fruitful. For these appli-cations the "one-sided" system of Fig. XVII-8 may prove useful.B. Howland(Mr. Bradford Howland is a staff member of Lincoln Laboratory, M.I.T.)QPR No. 71 273

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