RONALD N. BRACEWELL Vol. 45

FIG. 5. An auxiliaryconstruction for obtain-ing PT, a rough esti-mate of the next correc-tion term.

X

second derivative of g(x). This would mean that thespectral correction factor, as plotted on a diagram suchas Fig. 3, would increase indefinitely with s, and theformula has been criticized on this score. However, inpractice the formula is interpreted in terms of finitedifferences, and therefore, in the Gaussian case, the twomethods are identical and of identical accuracy.

ELABORATION OF THE METHOD

The term containing the fourth-order difference maybe evaluated by applying the chord construction to thesecond difference once it is plotted. This is quite feasible,as is numerical evaluation in many cases. However,retaining the approach of getting useful results forleast effort, we may ask, what graphical operation maybe made on the existing corrected curve which willindicate, albeit roughly, the magnitude of the nextcorrection term. This has a neat answer as follows.In Fig. 5, S is the corrected value corresponding to Pon the given curve. The point T is obtained by preciselythe construction used to get the broken curve, and willclearly fall close to P. Now by a slight adjustment ofthe chord span we may arrange for T to coincide withP where the correction is small. In other places, PTwill be proportional to the next correction term. Asthe details of this construction are different for eachcase, but simple, it will not be explained further.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 45, NUMBER 10 OCTOBER, 1955

One Million Frame per Second Camera*BERLYN BRIXNER

Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico(Received April 6, 1955)

The design and construction of a 1 000 000 fps (frame per second) rotating mirror frame camera is de-scribed. Twenty five consecutive pictures 20 mm in diameter can be obtained on a strip of 35 mm film. Aresolution of at least 20 lines/mm is obtained on a moderately fast film like Linagraph Shellburst. Accuratesynchronization of the event to be photographed is required. The camera has been most useful in the in-vestigation of explosive and related phenomena.

INTRODUCTION

THE 1 000 000 fps camera to be described was thefirst rotating mirror frame camera to be built

(1950) at the Los Alamos Scientific Laboratory andit has been in practically constant use in the investiga-tion of explosive and related phenomena for morethan 5 years. The successful operation of this camerais dependent on the use of explosive initiators whichcan be timed with an accuracy of a few microseconds,since the "seeing" time of the camera amounts to only12% of its cycle of operation. Luckily there are anumber of photoelectric trigger and pulse generatingcircuits suitable for the rapid firing of electric detonatorsand sychronization within 2 sec.

HISTORICAL

The pioneer rotating mirror frame camera withrefocused revolving beams was constructed by C. D.

* Work done under the auspices of the U. S. Atomic EnergyCommission.

Miller- 3 in 1939. This camera avoided "blind" spotsin the cycle of operation by the use of a multifacedrotating mirror and two images on the mirror face sothat as the edge between the mirror faces swept acrossthese images there would always be one completeimage recorded on the film. The linear picture sizewas therefore no more than half the size of the mirrorface which was in turn somewhat smaller than theperipheral diameter of the prismatic multifaced mirrorunit. The top speed of the camera is of course limitedby the bursting speed of the rotating mirror. Thefinal image was l in. in diameter and a maximum speedof 500 000 fps was attained.

The use of a dual optical system for refocusing therevolving beams was incorporated into a camera

I C. D. Miller, U. S. Pat. 2 400 887, May 28, 1946.2 C. D. Miller, "The optical system of the NACA 400 000-frame-

per-second motion-picture camera," National Advisory Com-mittee for Aeronautics, Technical Note No. 1405, 1947.

3 C. D. Miller, J. Soc. Motion Picture Engrs. 53, 479 (1949).

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ONE MILLION FRAME PER SECOND CAMERA

designed by I. S. Bowen4 and built in 1945. This designpermitted the image to be the full size of the mirrorface while still avoiding "blind" time in the cycle ofcamera operation. During part of the time, when theimage was split between two of the mirror faces, thetwo images were assembled at the film by means of aclever duplex optical arrangement. In practice theregistration of the two images to make the final picturewas somewhat imperfect, but nevertheless only a smallpercentage of the picture was duplicated on or lostfrom the final image. For a given image size the framerate could therefore be double that of the previouscamera. The final image was X 8 in. and a maximumspeed of 400 000 fps was attained.

In the meantime, excellent synchronizing anddetonator firing circuits had been developed so that asynchronizable rotating mirror frame camera waspractical for the investigation of explosive phenomena.One of the Bowen 76-lens frame cameras was borrowedand converted for operation at higher speeds. Thedual optical system and octagonal rotating mirror of thecamera were removed and replaced by a single opticalsystem and a two faced rotating mirror 5 for operationup to 5 000 rps. This increased the frame rate to over3 000 000 fps while at the same time the focus of theframing lenses was improved and better image qualityobtained. It was of course necessary to synchronizethe event to be photographed with the rotating mirror.The results obtained with this camera were so en-couraging that it was decided to construct a similarcamera for operation at about 1 000 000 fps, but withimproved space resolution. The description of thiscamera follows.

OPTICAL SYSTEM

The optical system of this camera is based on theuse of a rotating mirror and a refocused revolving lightbeam in a system which is a simplified version of thepioneer design by C. D. Miller.' Figure 1 shows aschematic diagram of the optical system used in thiscamera. Lens Li forms an image I, of the object to bephotographed, on or near the surface of the rotatingmirror RM after passage through the field lens L2. Thefield lens forms an image of the stop of the objectivelens Li at the framing lens L3, so that light from allparts of the image I, will simultaneously pass throughthe framing lens. As the mirror rotates it is seen thatthe light beam will pass successively through framinglenses L3A, L3B, L3c, etc. to form images I2A,

12B,

12C,

etc., in the film plane, after passage through the fieldflattener lenses L4A, L4B, L4C, etc. The field lens L2 isused to obtain the greatest efficiency from the opticalsystem. If it were not used, many of the rays from theedge of the image would miss the framing lenses and

I J. S. Stanton and M. D. Blatt, "The Bowen 76-lens camera,"NAVORD Report 1033, U. S. Naval Ordnance Test Station,Inyokern, Calif.

6 W. E. Buck, Rev. Sci. Instr. 25, 115 (1954).

FIG. 1. Optical v(( L L3 3A

diagram of onemillion frame persecond camera.

= RM~~~~~~RLi L2

result in a final picture which would be progressivelydarker toward the edge. Also the various rays wouldpass through the framing lens at different times (asthe mirror rotated) and hence prolong the exposuretime of the picture. Lenses Li, L2, and L3 are cementeddoublet achromats since these give excellent perform-ance over the small angular field needed. However,they result in a final image which is curved and it is toremedy this that the negative field flattener lenses areintroduced just ahead of the final image.6 Since theselenses are close to the focal plane they will have littleeffect on the aberrations of the optical system exceptthe Petzval curvature, on which their full power willbe effective for flattening the image plane. The imagerelaying (framing) lenses L3 are arranged to operateat 1:1 conjugates, but any other convenient valuecould have been used. The field flatteners somewhatovercorrect the distortion. Therefore it is necessary, inprecise work, to calibrate each frame for magnificationover the whole field.

It will be seen that any one of the lenses L 3 photo-graphs the real image which exists at the mirror. Theslight rotation of the mirror during a microsecond or sohas little effect on the position of the image. Rotationof the mirror, however, does provide shuttering andsequencing: a photograph can be made at one of the12 positions only while light comes through the framingstop at the associated relay lens. The images at 12 arethus not swept by the rotation of the mirror, butmerely light up and go out as the mirror turns.

The frame frequency, exposure time, and effectiveaperture of the camera are the most importantparameters for design consideration. The frame fre-quency of the camera is calculated as follows:

F= 2SN,

where F is the frame frequency in pictures per second,S is the mirror speed in revolutions per second, N is the

6 C. Piazza-Smythe, Brit. J. Phot., Almanack, p. 43-47 (1874).

877October 1955

BERLYN BRIXNER

number of framing lenses per circle. The rotatingmirror used in this camera operates up to 5000 rps andthere are 25 framing lenses in a 900 quadrant or 100per circle. The maximum frame frequency is therefore:

2X5000X 100= 1 000 000 fps.

With the framing lenses filling the circular arc as shownschematically in Fig. 1, and with the light beam thesame size as the lens, it is seen that the time requiredto sweep the light beam across a lens is twice thereciprocal of the frame frequency. If the lenses arerectangular in shape and the pupil in the revolvinglight beam is the same size, it is seen that a plot of theilluminated area of the lens as a function of time (Fig.2) gives a linear increase to the full lens aperture and alinear decrease to zero. The interval above half height onthis plot (75% of the exposure) gives a convenienteffective exposure time and this is simply the reciprocalof the frame frequency. The lens or the light beam maydiffer from the equivalent size that the lens would havein the fully filled arc, in which case the exposure iscalculated as follows:

E= diaF,

where E is the effective exposure time in seconds,d is the width of the lens or light beam in the directionof sweep, whichever is larger, a is the width of the lensin the fully packed case= 27rr/N, r is the radius ofthe relay lens arc.

This equation shows that for maximum exposure inminimum time, the stop at the relay lens should havethe same width as the light beam passing through it.The framing lenses used in the camera were fullypacked (Fig. 4) and hence the minimum effectiveexposure time for the whole lens was 1 sec. However,

B A

I \V/~~~\ / \ -4

it was found that satisfactory exposures could beobtained with much less aperture, and diamond-shapedstops7 were installed to give an effective exposure timeof:

0.6-d 0.6.5E= - = = 0.14 sec.

a-F 21-106

The advantage of the diamond stop can be seen by aconsideration of Fig. 2. Assume a rectangular framinglens A and a rectangular light beam B swept across itin the direction of the arrow. The upper curve showsa plot of the area common to the two rectangles as afunction of time. Now consider the case in which thelens and light beams are in the shape of the inscribeddiamond shown. The plot of this is the lower curve onthe graph. The resolving power of the lens with thediamond aperture has been found to be about 0.8 thatof the lens with the rectangle. The common area plot,however, is found to have a width at height of only0.6 of the rectangular case and an area of about 0.35.The effective exposure time can, therefore, be reducedto 60% with a tolerable loss in optical resolution if onecan afford to reduce the exposure to about 35%. Ifthe long dimension of the diamond can be increasedto make the area of the diamond equal to the rectangleit is seen that there is no loss of aperture while theexposure time remains at 0.6. In any case, the use ofdiamond-shaped stops is not vital to the efficientperformance of the optical system since the gain issmall. Stops of various sizes have been used for differentproblems. Small stops are indicated when the objectcontrast and brightness are high.

The maximum aperture of the camera is limited bythe relay lenses which in this case have an aperture off/16 in the direction of the sweeping light beam by f/11in the direction at right angles. The mean effectiveaperture is about f/13. The effective aperture with

FIG. 2. Aperture-timecurve for optical shutterused in camera.

FIG. 3. Exterior of one million frame per second camera.

7 The use of diamond stops was suggested by T. E. Holland,Los Alamos Scientific Laboratory, University of California,Los Alamos, New Mexico.

878 Vol. 45

ONE MILLION FRAME PER SECOND CAMERA

FIG. 4. Interior of camera with film loaded.

the diamond stop is about f/40 but this is quiteadequate for much of the work if high-explosive argonlight sources8 are used.

CAMERA CONSTRUCTION

The completed camera, which is about 1X3X5 feetin over-all size, is shown in Fig. 3. The photoelectricsynchronizing unit is mounted on the side of the cameraat the lower left. The 1/50 sec mechanical shutter withits electrical release and shutter position informercontact is shown in the lower right. The objectivelens tube and focusing mount is shown at the extremelower right. The synchronizer operates from a mirroron the end of the turbine shaft. This synchronizermirror is made by cutting the turbine shaft off atabout 10° from the normal to its axis and polishing toform an optically flat mirror. A lens forms an enlargedimage of the filament of a miniature incandescent lightafter reflection from the mirror on the end of the shaft.As the shaft revolves the image will sweep in a circulararc. A slit aperture is placed along this arc and thephotoelectric tube beyond that. This arrangementproduces a pulse during each revolution of the shaftand can be phased by rotation of the synchronizerunit about the shaft axis.

Figure 4 shows the interior of the camera after theside has been removed. Light enters through themechanical shutter at the lower right and forms an

8A. Michel-Levy and N. Muraour, Compt. rend. 198, 1499and 2091 (1934).

FIG. 5. Interior of camera with framing lens stops in position.

image of the object being studied on the rotating mirrorshown in the lower left part of the camera. Field lensL2 is located at the hole in the partition adjacent tothe mirror; a segment at the top has been cut off toavoid interference with the reflected beam at the endof the lens ring. The 25 relay lenses on the inner arc arecut to 21 mm width and packed solidly into place.Each of these lenses consist of two cemented doubletachromats of 344-mm focal length by 34 mm diameter.These lenses form the final images on the 35-mm filmwhich is shown loaded into position. Figure 5 is similarto the previous figure except that the diamond-shapeddiaphragm stops are in place over the relay lenses. Thisstop is easily moved into position by means of a knobon the outside of the camera. The film has been removedto show the field flattener lenses, which are mounted inthreaded cells to facilitate setting the plano backsurface in the best focal plane. When the film is loadedover these lenses it is stretched sufficiently tight to bein contact with all the lenses. The maximum image sizeis limited by the rotating mirror or these lenses whichare 20 mm in diameter. The resolution on the Shell-burst Linagraph film negative was found to be not lessthan 20 lines/mm for the entire picture area of all theframes.

The operation of the camera for picture taking is asfollows. The photoelectric synchronizer is set to fire thelight source to be used or the explosive charge to bestudied at such time that the mirror will be in thecorrect position to start making photographs. The lens

October 1955 879

BERLYN BRIXNER

FIG. 6. Photographs showing primacordexplosive shutter operation.

will have been focused on the object being studied, theshutter cocked, the film loaded, power supplied toelectrical control system, and the turbine set intooperation at the required speed. The mechanicalshutter is tripped by a signal from the control paneland, as soon as it has opened, a set of contacts areclosed by it to give continuity to the synchronizerpulses so that they may be used to trip the high voltagesource used for the light source or for firing the explosivedetonator. The sequence of pictures is made as themechanical capping shutter continues to close; in factwhen explosives are used multiple exposure wouldusually occur if a very fast shutter were not provided.Such a fast shutter' is made by detonating primacordexplosive fuse at a point near the window whichprotects the camera from the explosive shock wave.The explosive of the primacord produces an opaque,conical shaped shock wave enclosing a smoke cloud.The opacity persists until the smoke is dissipated byconvection or by shock waves from the main charge.

SAMPLE PHOTOGRAPHS

The photographs in Fig. 6 show the operation of theprimacord explosive shutter used in connection withhigh speed rotating mirror cameras. Two pieces ofprimacord (approximately 6 mm in diameter) arestretched across the window to be shuttered. These arethen detonated so that the shock waves will be at thewindow when the shuttering action is required. Thefirst photograph shows the exploding primacordsilhouetted in front of an argon explosive light source.The detonation has progressed to points just inside thewindow area and the opaque, conical shock wave from

I A. W. Campbell, U. S. Patent 2470139, May 17, 1949.

the primacord is clearly shown. The detonation ismoving to the right along the upper primacord and tothe left on the lower one. Succeeding photographs showthe movement of the shock wave and the progressiveenlargement of the opaque area in front of the window.The photographs were taken at the rate of 1 000 000fps but only every third frame is shown in this series.

DISCUSSION

The simple design of this camera makes possiblealternative models with a wide range of picture size,frame frequency, total number of frames, relativeaperture of the lens system, and accommodation of thedesign to available optical elements. The latter pointis a matter of practical importance since the use ofstock lenses usually facilitates procurement and avoidsthe need for the tight manufacturing tolerances oftenrequired in a custom design. Other cameras have beenmade at the Los Alamos Scientific Laboratory withpicture sizes ranging from 6 to 25 mm, number offrames from 48 to 170, and frame frequencies from5-104 /sec to 1.5.107 /sec. This range by no meanspretends to be the attainable limit but is rather theresult of particular recording requirements. The designsimplicity is achieved at the expense of synchronizingthe event to be photographed with the rotating mirror.

ACKNOWLEDGMENTS 11^

The construction of this camera was a team projectby the members of the Optics Group and the authorwishes to express his indebtedness to Mr. W. E. Buckand Mr. R. W. Prichard for the design and fabricationof the rotating mirror drive and synchronizer withoutwhich this camera would be relatively useless, Mr. A. J.Lipinski for the optical calculations and measurements,Mr. A. N. Strein for the preparation of engineeringdrawings, Mr. S. I. Rochwite for the design and con-struction of the mechanical shutter and objectivelens focusing mount, Mr. G. H. Schultz's machine shopfor fabrication of the camera, Mr. L. M. Gardner'sGraphic Arts Group for preparation of the illustrations,Dr. F. J. Willig's group for the preparation of the samplephotographs of explosive phenomena, Dr. F. A. Lucyfor reviewing this paper and making valuablesuggestions, and Dr. D. P. MacDougall for encouragingthe development of rotating mirror frame cameras atthe Los Alamos Scientific Laboratory.

880 Vol. 45