Spie Press BookRotating-Mirror Streak and Framing Cameras
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- Part I: BASIC STREAK CAMERA DESIGN...1
- Purpose and Use of Field Lenses...1
- Geometry and Parameter Identification for Simple Streak Cameras...14
- A Methodology for Constant Writing Rate...16
- Retrofitting Rotating Mirrors in Streak Cameras...20
- Positioning Tolerances for Streak Camera Parameters...36
- Analysis of Streak Camera Measurement...39
- Absolute and Relative Error Evaluation...44
- Implications of the Total Incremental Velocity Error...49
- Demonstration of an Asymmetrical Recording...49
- A Streak Camera Design Operationally Invariant to Mirror Size and Location...53
- Part II: BASIC FRAMING CAMERA DESIGN...58
- Retrofitting Rotating Mirrors in Framing Cameras...65
- Geometries for Pupil Formation...77
- Image Motion Behavior...85
- Selected Bibliography...107
During the past few years some time was devoted to reviewing earlier work spent in the design and development of high-speed optical recording devices while one of the authors (Igel) was at Los Alamos National Laboratory, Lawrence Livermore National Laboratories, and Sandia National Laboratories. This earlier work, relating to rotating mirror streak and framing cameras, comprised a series of notes and internal reports that could have served as the genesis for conference papers. Their expansion and collection here forms this monograph, and, as a result, imparts a somewhat independent chaptorial reading. This collection does not provide a historical development of camera systems nor does it attempt to provide an inclusive account of how to completely engineer, use, and care for high-speed recording devices, which, of course, are most important subjects in their own right. Instead, we assume the reader has some background in the type of high-speed recording devices discussed, and we hopefully present particular insights and design directions for those who have either built or understand the basic design concepts of high-speed rotating mirror cameras. Nevertheless, we believe sufficient detail and structure exists in this monograph to allow the less experienced but determined reader to become familiar with particular design criteria for high-speed rotating mirror streak and framing cameras. For those not familiar with these devices, we will list a simplistic arrangement of their main constituent parts with the hope of giving the reader an awareness and sense for their overall simplicity and applicability. Anyone can start to assemble a somewhat workable streak camera by sequentially attaching an objective lens, slit, field lens, relay lens, and rotating mirror to a rigid rail or track. The objective lens forms an image of the event under study on the slit. The field lens that lies adjacent to the slit images the objective lens onto the relay lens that in turn images the slit via the rotating mirror onto a circular recording surface. The slit assembly may be formed by spacing a pair of single-edged razor blades one or two tenths of a millimeter apart to form a slit running the length of the blades. The field lens lies in the image plane at the slit, and the function of this lens is to image the exit pupil of the objective lens onto the entrance pupil of the relay lens. This effect is accomplished when the field lens refracts off-axis image-forming cones of light, i.e., the image points away from the center of the slit, back toward the center of the relay lens as discussed later in the text. Field lenses are useful anytime one needs to relay unvignetted images, as exemplified by their use in optical delay paths and periscopic systems. Note that field lenses have a long history and are necessary constructs in two old popular oculars, known as the Ramsden and Huygens eyepieces. In the Ramsden eyepiece, an image plane lies a short distance before (in front of) the field lens, which is followed by the eye lens, and in the Huygens eyepiece an image is formed a short distance after (behind) the field lens and this image is then viewed by the eye lens. In either case, the field lens refracts cones of light from off-axis image points toward and into the eye lens, and thus forms in conjunction with the eye lens an exit pupil at the observer's eye pupil. The streak camera's relay lens should ideally form an image of the slit at about unit magnification, and this may be accomplished by taking two achromatic lenses of equal focal length with their crown elements closely facing and positioning the lens-pair an original one focal length distance from the slit. A small rotating mirror having an integral cylindrical shaft may be attached to a variable high-speed electric grinder motor. The rotatable mirror is positioned near but behind the symmetrical achromatic lens pair, and the image of the slit is now reflected from this mirror, which sweeps out an approximate right circular cylindrical image path. Any detector, e.g., photographic film, placed on this image path records the temporal location of the slit. Conversely, if the slit is imaged in the opposite direction by the objective lens, then a stationary line object is focused in an object space at which location the subjects under study should be placed. This projected line object is a pre-event condition temporarily realizable by illuminating the slit in such a fashion as to project light into the objective lens. Note that this line object delineates the area on the subject or subjects under study that will be dynamically swept across the detector (film) by the rotating mirror. With this camera we could, for example, look at a linear array of flash bulbs and determine the asimultaneity of their central flashes or we could with magnification look at a line across a single bulb to determine the propagation of the illuminating phenomenon as it engulfs the entire bulb. A static image of the slit at the detector (film) defines the spatial axis, and the rotating mirror traces a temporal axis for any point along the slit. Clearly, event velocities are obtainable from this rectangular coordinate system of distance and time when we know the magnification of the optical system that converts distance at the detector (film) to distance at the object or event under study.
With an ideal optical system and a flat rotating mirror, the camera's spatial resolution in terms of line pairs per millimeter is proportional to the half-angle of the image-forming cone of light. The size of the camera's image-forming cones of light are normally limited by the size of the rotating mirror. In practice the quality of the waveforms of the image-forming cones of light are also an important factor in determining resolution. The temporal resolution is defined by the ratio of twice the width of the slit to the writing speed, i.e., the time for the slit to traverse itself at its calculated linear sweep velocity. Note that the tensile strength of the material used for the rotating mirror, mirror size, and the distance of the mirror to the recording surface determine values for both the cone angle of the image-forming beam and the mirror's maximum angular velocity which in turn is proportional to the writing speed at the recording surface. The sine of the half-angle of the image-forming beam is proportional to image resolution in line pairs per millimeter, and the reciprocal of this image resolution established the minimum slit width, the value of which when doubled and divided by a practical maximum writing speed (from mirrors of high-strength steels) gives a theoretical time resolution of 0.9 ns. For a given mirror material and an assumed dynamically undistorted mirror face, the ratio of minimum slit width to maximum slit velocity is invariant with mirror size. Here, the maximum slit velocity is based on the mirrors perpheral velocity being limited to a speed of Mach 1 at standard conditions. This limit is pragmatic, although not the mirror's burst speed. Even with sophisticated rotating mirror cameras, realizing temporal resolution of a few to several nanoseconds takes prudent care. For the purist, our temporal resolution limit differs from the "Schardin Limit" by the product of twice the diffraction constant of 1.22. The basic difference is obtained because we specify time resolution as the time for the leading edge of the slit image to traverse a distance equal to twice its own width.
In most camera applications, the slit width is made larger than the allowed minimum width to obtain a photographic record while accepting the penalty of degraded time resolution. Increasing the slit width increases exposure time and, thus, the exposure (energy per unit area) of the photographic film. Exposure is a product of exposure time and the final image irradiance (power per unit area), and the exposure of the film must always exceed the film's rated recording threshold, energy per unit area to produce a given film density. For extended images the image irradiance at the film is proportional to both object radiance (power output per unit area per unit solid angle) and the square of the half-angle of the image-forming cone of light that forms the slit image. We may, of course, calculate with the given camera parameters the object radiance necessary to equal or exceed the recording threshold. Knowing the camera's optical transmission function, i.e., transmission as a function of wavelength, also allows us to define this required radiance in terms of the equivalent blackbody temperature that the object must reach to produce an exposure on a given film.
Measurement errors of the recorded space-time analog can be significant and are caused by misalignment of camera parameters and the inability to define well the leading edges of recorded information. Very briefly, the axes of the rotating mirror, cylindrically circular focal surface (film track) and the slit should be perpendicular to a selected reference plane (1 mrad is a realistic and satisfactory goal). The coordinate positions for the camera parameters as projected onto the selected reference plane are discussed in the following sections. Measurements to confirm adequacy of the linearity of the sweep or time axis and its perpendicularity to the slit image are easily made and should be done. Static spatial resolution measurements should and can easily be made at several locations along the recording track to confirm adequacy of focus.
More subtle are the factors leading to degradation of image contrast. In general, defocusing caused by dynamic mirror distortion is a serious problem. Fortuitously, a flat steel rotating mirror distorts to a shape approximating a right circular cylinder, and thus the addition of a cylindrical lens between the slit and relay lens can markedly compensate for the otherwise large loss in temporal resolution. The use of a beryllium mirror with small Poisson's ratio negates for the most part the mirror distortion problem. Thus, the need for optical compensation is alleviated. More insidious to image degradation are diffracted, reflected, and scattered light from the edges and/or surfaces of the slit, lens apertures, baffles, rotating mirror, and camera housing. The relative intensity of diffracted and scattered light is unfortunately large because we are often dealing with object radiances equal to several suns. Furthermore, the source of extraneous light usually has a duration many orders of magnitude greater than the actual recording time. An image formed by an object of high radiance is delineated by a slit having ample opportunity, if not carefully crafted, to reflect and scatter light at its edges and face. Image beams within the camera are often intercepted by inappropriately located stops or baffles, dirty and dusty windows, lenses, etc., as well as by a dirty or dusty rotating mirror, all of which reduce the image contrast. Even the interior of the camera housing itself can contribute to this problem. Attention to these details is well rewarded but rarely lauded. Refractions due to the compression of the gas medium (usually air) by the peripheral speed of the rotating mirror (as high as Mach 1) also can take a toll on both temporal and spatial resolution. Such refractions are minimized when the rotating mirror is operated in a medium of helium. Of some concern are the similar deleterious refractions surrounding an explosive object when one looks through compressed gases to a surface under study. The somewhat gratuitous mitigative effect in this latter circumstance is simply the location of the disturbing medium, i.e., close to the object plane. As a matter of principle, a suspect surface, e.g., a turning mirror and/or refractive window, should be located as close as possible to either image or object space where the lever arm of any deviated ray is small relative to the image or object plane. Even though the streak camera is elegantly simple, investigations using this device can be sophisticated, particularly when a single slit is replaced by linear slit arrays. If multiple parallel slits are projected into an object space, then two mirrors at right angles (corner mirrors) can wrap these lines around several circumferences of an object in the form of a right circular cylinder, or if the cylinder is rotated 90 deg, the projected slit lines could strike the periphery of the cylindrical surface to form a series of lines parallel to the cylinder-axis. An unusual slit plate in the form of concentric circles could be used to project its pattern onto any flat object surface or onto a spherical object when allowed by the depth of field. Another scheme would feature a fiber optic bundle designed to transform any projected geometric pattern in object space into a single or multiple slit array as input to the relay lens of the camera. Removing the slit plate completely from the camera provides a two-dimensional view of an object space. If this space contains an object designed to emit short-lived bursts of light from designated and documented elemental areas, then an assessment of their simultaneity can easily be made with no slit in place. Note that whenever a single slit is not used, then the issue of rewrite or overwrite becomes a problem. Overwrite may be alleviated by providing a mechanism at the object to limit the time duration of the light emissions or, alternatively, one might consider limiting the camera's recording time by a fast shuttering mechanism. If discrete explosive systems are under study, a transparent barrier such as Lucite or Lexan can be used to quench the light emission when the barrier is placed a short distance (one or two tenths of a millimeter) from an explosive surface, i.e., at least attenuating the light signal to a level below recording threshold after the shock front strikes the barrier. An ancillary benefit to this scheme is that the light signal is enhanced as the shock increases the pressure and thus temperature as contact is made with the barrier. If particular elemental areas on an extended explosive surface are under study with a multiple-slit streak camera, then to prevent overwrite we could use the strategy of markedly enhancing for a short time interval the light emissions from the particular areas under study by using the nobel gases, e.g., argon or krypton. This allows the camera's recording threshold to be set at a level to record only the particular high-radiance short-lived elemental areas. In those experiments where extraneous lighting can be provided as the recording power source, then appropriately timed short duration bursts of light may negate the problem of overwrite. In general, whenever an object space is to be time resolved, a streak camera should be a first consideration and is often the indispensable device.
Spatial and focal identification of the object under study is often essential to understanding and correctly interpreting a streak camera recording. One method of composing and focusing an object is to view it with a compound microscope on a slightly inclined and mirrored slit plate that contains a transparent slit. Once alignment is judged satisfactory, a static image of the slit is recorded. Then the slit plate can be removed and replaced with one having only a transparent field. Photographic documentation of the object will then identify the slit location relative to the object as well as the magnification of the final image. Alternatively, if one has a slit plate that contains an opaque line on a transparent field with the line having been indexed to match the slit location, then the object may be composed, focused, and recorded at the final recording surface. An ancillary scheme for composing the object entails projecting light, e.g., using laser diodes, back through the camera system to delineate in object space the precise areas of the object from which light can be recorded. This probably means having to make observations in subdued light, but the physical scene showing what one is actually photographing is often an important realization. Final recorded documentation could be carried out by one of the two previous methods.
The sequential and integral sampling of a two-dimensional object space is the domain of the framing camera. Many motion picture cameras with formats from 8 to 70 mm have framing rates from hundreds to many thousands of frames per second. High- speed rotating mirror cameras cover the recording range of hundreds of thousands to tens of millions of frames per second. Anyone can assemble a poorly workable but instructive framing camera by moving the rotating mirror in a streak camera to that axial position where the slit image would be focused by the relay lens. Because typically an objective lens focuses a two-dimensional image of object space onto the slit, the slit's removal from the optical system allows the relay lens to present or focus this two- dimensional image on the newly positioned rotating mirror. A series of adjacently placed box cameras, e.g., 35-mm cameras, arranged in a semicircle with the rotating mirror at the center produces a crude framing camera when all individual cameras are focused on the rotating mirror. Now, when the mirror rotates, a circular patch of light is swept along and over the arc of 35-mm cameras. The instructive principle here is that the patch of revolving light is larger than the individual 35-mm camera lenses and may often encompass several camera lenses at any one point in time. Thus, not only are several 35-mm cameras recording the same picture at any given time, but the exposure time of each 35-mm camera is maximum and equal to the sum of the diameters of the patch of light and the 35-mm camera lens divided by the patch's peripheral velocity. Note that the reciprocal of the exposure time is equal to the recording frequency in terms of the number of meaningful pictures or frames recorded per unit of time. Miller discussed and filed a patent for a well-designed framing camera in 1946 using an optical scheme that condensed the above-mentioned revolving patch of light to a size that in our discussion would match the size of the 35-mm camera lenses without compromising resolution and recording irradiance. The artifice here lies in having all cones of light forming the extended image at the rotating mirror converge instead of diverge after reflection to form a minimum common-sized pupil area at the 35-mm camera lenses. This general scheme of superposition is called pupil control or pupil matching, and one method of attaining this goal is by adding a lens (achromat) between the relay lens and the rotating mirror with the achromat as close as possible to the rotating mirror without blocking the beams reflecting from the mirror. In this position the achromat behaves like a pseudofield lens in that it is proximate to an image plane and has the primary aim of imaging the exit pupil of the relay lens onto the entrance pupil of the 35-mm camera lens. In this discussion we will adopt a simplistic and crudely approximate optical reality by assigning the location of the relay lens' and 35- mm camera lens' pupils to their respective rear and front optical elements. Therefore, using the Gaussian form of the lens equation, we may calculate the required focal length for the achromat by knowing both the achromat's fixed object distance to the relay lens and its operating magnification specified by the ratio of the achromat's distances to 35- mm camera lens and to the relay lens. The size of the relay lens pupil would be adjusted to match the size of the 35-mm camera lens. A simple optical modification is obtained when the relay lens, field lens at the former slit position, and the objective lens are replaced with another objective lens to focus the original object directly onto the rotating mirror with the aid of optical power from the achromat positioned in front of the rotating mirror. An appropriately sized aperture defining a pupil would be placed proximate to the front or rear of the objective lens. This camera's simplicity (minimum number of lenses) may be offset by restrictions imposed on the objective lens' range of operational magnification, and when exceeded, requires internal adjustments to the pupil and achromat positions. Returning to the modified streak camera layout with the relay and objective lenses and with the rotating mirror at the former image of the slit, we can envision a still different and useful geometry for pupil control when an aperture defining an entrance pupil is located between the relay lens and the former slit position. As before, an objective lens makes an image of the object under study in front of the pupil, and this image plane should contain a field lens (details of which are discussed later) to image the objective lens onto the following defining pupil, i.e., the entrance pupil of the relay lens. Then the relay lens can perform two functions: focus the entrance pupil via the rotating mirror onto the 35-mm camera lenses, and relay and focus the image from the objective lens onto the rotating mirror. The significant benefit from this geometry is the elimination of the need for the achromat in front of the rotating mirror. However, such a scheme does require a large-aperture relay lens that would operate at other than unit magnification. For the experimentalist, an hour or two on a lens bench demonstrates the likelihood of image vignetting as well as the innumerable tradeoffs for image and image beam sizes that nevertheless are always governed by the Lagrange invariant, i.e., the product of image height and image-forming beam is invariant within a given medium.
Extraneously scattered and refracted light, as in a streak camera, can degrade the final image contrast. A rotating mirror that is dusty, smudged by a film of oil, or abraded by usage will scatter a large amount of light. This effect is particularly serious in a framing camera because an image of high irradiance is focused on the rotating mirror and all scattered light is now seen as an image source. Therefore, interior cleanliness of the camera and its components should be a high-priority exercise. Dynamic mirror distortion and index gradients surrounding the rotating mirror deserve less consideration in a framing camera than in a streak camera. Again, remember unwanted deviations of any ray are minimized when the angular aberrations occur near the image plane at the rotating mirror because the apparent displacement error for any given image point is the product of the angular deviation and the lever arm. Clearly, the lever arm is orders of magnitude smaller for framing cameras than for streak cameras.
The ultimate design consideration for these recording devices often is their ease of use. The ability to select the exact portion of the object one wishes to record and to obtain exacting focus easily and confidently is of prime importance and usually determines the quality of information gathered. As briefly mentioned earlier, with a streak camera we should record a static image of the slit along with a scale for determining system magnification. Also needed is a dynamic image of the sweep or time axis. With a framing camera, a selected frame should be dedicated to recording a magnification scale. When possible, add light sources in an object space to provide a magnification recording. Reference points offered by the extremities of a cross hair on each frame (picture) as a pre- or postexposure are vital to measurement accuracy and when accomplished dynamically, so much the better. Unfortunately, such a reference is rarely offered.
Whenever we are limited by the subject's radiance and the detector's recording threshold and have already made the angle of the image-forming cones of light and exposure time as large as possible, then we must intensify the object and/or image. Object intensifiers in the form of noble gases, aluminum/magnesium silicates, etc., are often the most expedient way to increase object radiance. Fiber optic coupled image intensifiers satisfy most image resolution requirements, although implementation is costly. Use of extraneous front or back lighting at the object sometimes in combination with schlieren, shadowgraphic, or interferometic techniques can provide, if not direct often indirect, evidence of the information sought. Clearly, the ingenuity of the investigator always amplifies the value of the instrumental recording.
A large number of rotating mirror cameras have been manufactured in the last several decades to cover a range of recording demands often near the limits of the rotating mirror's burst speed. Many experiments demand the highest recording rates possible, and this demand has been generally satisfied by optoelectric devices, such as image-converter cameras. Nevertheless, a large class of phenomena still exist with temporal and spatial details that can be documented better by optomechanical cameras. In Part I, a brief review of the principles of design for rotating mirror streak cameras is given along with an explanation of the need and choices for using a field lens. Options for successfully relaying images are explained in detail. Although somewhat application limited, an expression is presented to achieve a constant writing speed for streak cameras by giving the image of the field stop (slit) contra-accelerated motion while it is being imaged by the relay lens via the rotating mirror onto the focal surface. The major thrust of this monograph is to explore strategies to retrofit rotating mirrors that are sized differently from the original design. Using smaller rotating mirrors in streak cameras offers high writing rates at the expense of smaller cone angles for the recording beams. This in turn reduces both the information and irradiance levels carried by these recording beams; however, this is very often an acceptable penalty for obtaining an increase in writing speed. Installing smaller rotating mirrors in framing cameras offers higher framing rates with, however, attendant loss of information because the mirror size limits the image size, which proportionally defines the total number of information bits contained in each picture. Nevertheless, some circumstances offer real investigative advantages to the use of smaller rotating mirrors. Using a mirror larger than the original design is not a viable replacement option, because the required constructional modifications to the camera to accommodate a larger rotating mirror as well as the resultant larger image sizes at the film are just not cost effective. Conversely, smaller mirrors and their associated turbine drives can be installed without remachining the camera housing. Furthermore, alteration of the camera's existing lenses and film format to accommodate the new imagery is not necessary. One facet of streak camera design involves assessing the relative importance of the camera's positioning variables to maintain a specified writing speed. Awareness of the tolerances allowed for each positioning variable influences constructional choices, and this consideration could increase the quality/cost effectiveness of the instrument. Analyses of streak camera records are discussed with particular emphasis placed on errors contributed by the lack of slit orthogonality to the recording axis in combination with the chosen strategy for measuring or extracting information. An example is given to show how symmetrical event phenomena can be asymmetrically recorded and subsequently restored with knowledge of the slit misorientation angle. Most streak cameras have their rotating mirror placed in converging cones of light that subsequently focus on a circular focal surface. Interesting features result when the rotating mirror is placed in collimated bundles of light that after reflection from the mirror traverse a lens that focuses the image onto a plane focal surface. Once focus is established, the shape and position of this flat focal surface in invariant to size or location of any replacement mirror as are the nonlinearities of slit image size and velocity.
Considerations for a layout design of a rotating mirror framing camera are discussed with emphasis placed on location of the framing relay lens arc and the magnitude of the image motion generated proximate to the mirror. The location of the mirror's rotational axis relative to the static image markedly affects system performance, and geometric aberrations are evaluated for a typically used geometry with the results graphically presented. A methodology is then developed to retrofit differently sized rotating mirrors to an existing camera. The analysis infers that benefits accrue when microadjustments are provided for fine-tuning the location of the axis of any finite-sized rotating mirror. Such adjustments might be included in the original design and are perhaps an overlooked sophistication that can add significantly to photographic excellence. This excellence is obtained for synchronized recording systems when microadjustments to the rotating mirror peak the image resolution at a chosen specific location on the recording arc. Various pupil geometries for the framing lenses are discussed and a unique X-shaped geometry is proposed for reducing the exposure time of framing cameras while maintaining the peak irradiance offered by the normally used diamond-shaped pupil. The exposure functions of several different pupils are presented and judgments made. Having placed a rotating mirror of finite thickness at its optimum location, we still always find residual image motion as seen by the framing lens. The elemental coordinates of this motion are analyzed as a function of the mirror's positional coordinates as well as its angular position, thickness, necessary angular sweep to complete an exposure and image size at the mirror. Graphical examples of this aberration are given, and predictions of image resolution are made for a camera employing rectangular pupils. A discussion follows to assess possible remedies for increasing image resolution at the detector.
Although discussions in this monograph are restricted to in-plane recording systems that constitute the bulk of existing instrumentation, the principles outlined can be extended to cover our-of-plane recording systems (nonperpendicularity between rotating mirror and lens axes). The authors realize this monograph is limited in scope, but hope that attention will be drawn to a few colorful spots of instruction and advancement.