HOLOGRAPHY AND HOLOGRAPHIC INSTRUMENTS

This is continuation from the previous tutorial - Polarimetry

 

 

1.  INTRODUCTION

The three-dimensional imagery produced by holography accounts for most of the current popular interest in this technique. Conceptual applications, such as the holodeck seen on the television series Star Trek:

The Next Generation, and actual applications, like the widespread use of embossed holograms on book and magazine covers and credit cards, have fascinated and captured the imagination of millions. Holography was discovered in 1947 by Gabor and revived in the early 1960s through the work of Leith and Upatnieks. Since that time, most practitioners in the field believe that technical applications, rather than imaging, have represented the utility of holography in a more significant way.

This tutorial is a brief overview of some of the more important technical applications, particularly as they relate to a variety of instrumentation problems. The discussion addresses several ways holography has been used to observe, detect, inspect, measure, or record numerous physical phenomena.

The second section presents a brief review of the basic principles of wavefront reconstruction. The third section addresses what is undoubtedly the most important application of holography to date—holographic interferometry.

This is followed by a review of electronic or television holography (the fourth section) which takes this powerful interferometric technique into the real-time domain. The fifth section addresses several instrumental applications of holographic optical elements \(\text{(HOEs)}\). The sixth and seventh discuss ways in which holography is being applied in the semiconductor industry.

The final section briefly addresses the holographic storage of information.

 

 

2.  BACKGROUND AND BASIC PRINCIPLES

Holography is a method of recording and reconstructing wavefronts residing anywhere in the electromagnetic spectrum or acoustic spectrum. This tutorial addresses optical holography as practiced in or near the visible region of the electromagnetic spectrum.

The principals of wavefront reconstruction were discovered by Gabor in an attempt to improve the resolving power of the electron microscope. The original purpose was never accomplished, but this basic discovery evolved into one of the most significant new fields of study in this century. Gabor’s early work received little attention because the lack of a light source with sufficient coherence severely limited the quality of the images produced.

However, the invention of the laser in the early 1960s heralded a holographic renaissance. During this period, Leith and Upatnieks recognized the parallels between their work in coherent radar and Gabor’s wavefront reconstruction concepts.

Their experiments in the optical region of the spectrum with the newly available \(\text{HeNe}\) laser produced the first high-quality, three-dimensional images. The publication of this work created an explosive interest in the field as well as many unrealistic predictions about what might be accomplished with holographic three-dimensional imagery.

The work of numerous researchers established the medium’s true capabilities and limitations; consequently, many successful applications ensued. Progress continues to be made in the development of new materials and techniques sustaining a high level of interest in holography and its technical, commercial, and artistic applications. 

Holography is most often associated with its ability to produce striking three dimensional images. Therefore, a logical place to start in understanding holography is to compare this imaging science with its two-dimensional predecessor—photography.

A light wavefront is characterized by several parameters; the two most important of these are its intensity (or irradiance) and its local direction of propagation. Photography records only one of these parameters—intensity—in the plane of the recording medium or photographic film. The intensity distribution of a light wave emanating from an object may be recorded 

 

 

by simply exposing a film plate placed in proximity to the object; however, this will not produce a discernible image. Recording a photograph is accomplished by imaging the object onto the film with a lens, thereby establishing a correspondence between points on the object and points in the film plane.

Holography also records the intensity distribution of a wavefront; in addition, the local propagation direction (or phase) is recorded through the process of optical interference. The process in its simplest form is illustrated in Fig. 1. The light from a laser is split into two parts, expanded with a short-focal-length lens (usually a microscope objective), and spatially filtered with a pinhole to remove intensity variations caused primarily by nonuniformities in the lens.

One of the split beams (object beam) is directed to the object; the other (reference beam) is incident directly on the recording medium (such as a high-resolution silver halide film). The light reflected from and scattered by the object combines with the reference beam at the plate to form an interference fringe field. These fringes are recorded by the film. The spacing of these fringes d is given by the grating equation

\[\tag{1}d=\frac{\lambda}{(\sin\theta_1+\sin\theta_2)}\]

where \(\lambda\) is the wavelength of the light, and \(\theta_1\) and \(\theta_2\) are the angles made by the object and reference beams relative to the normal. For visible light and common recording geometries, the fringe frequency \((1/d)\) can exceed 2000 fringes (or line-pairs) per millimeter.

Therefore, the recording material must be of very high resolution relative to conventional photographic film which is usually in the range of 50 line-pairs per millimeter. The stability of the fringe is extremely sensitive to the mechanical motion of the object and optical components.

To record holograms with good fringe stability, the optical system must be stable enough to prevent motions greater than a fraction of a wavelength.

For this reason, the common practice is to use rigid optical components placed on a stable, vibration-isolated table.

Illumination of the developed hologram by the reference beam alone reveals a three-dimensional image which is essentially identical to the original object as viewed in laser light. Observing the holographic image of the object is exactly like looking at the object through the window formed by the plate with full parallax and look-around capability.

The object wave is reconstructed when the illumination (reference) wave is diffracted by the grating formed in the recording medium. This grating is formed by variation of the optical transmittance or optical thickness of the material along the fringe lines.

The amplitude hologram formed with silver halide film may be converted to a phase hologram by bleaching; this results in a significant increase in diffraction efficiency. Other materials (such as photopolymer film) produce phase holograms directly.

The holographic recording and reconstruction process may be described in general mathematical terms as follows. The object and reference fields satisfy the Helmholtz equation

\[\tag{2}\nabla^2\boldsymbol{E}+\text{k}^2\boldsymbol{E}=0\]

where \(\boldsymbol{E}\) is the electric field vector and \(k=2\pi/\lambda\) is the propagation constant. 

A spherical wave solution of this equation may be expressed in the form

\[\tag{3}\boldsymbol{E}=Ae^{ikr}\boldsymbol{e}^{i2\pi ft}\hat{\boldsymbol{e}}\]

where \(A\) is the amplitude of the wave, \(f\) is the frequency, and \(\hat{\boldsymbol{e}}\) is the polarization unit vector. 

The complex field amplitude \(\Psi\) is defined as

\[\tag{4}\Psi=Ae^{i\phi}\]

where \(\phi=kr\) is the phase. The irradiance of the field is given by

\[\tag{5}\begin{align}I&=\boldsymbol{E}\cdot\boldsymbol{E}^*=\Psi\Psi^*\hat{\boldsymbol{e}}\cdot\hat{\boldsymbol{e}}=\Psi\Psi^*\\&=A^2=|\Psi|^2\end{align}\]

where \(^*\) denotes the complex conjugate.

The field in the plane of the hologram \(\Psi_H\) is the sum of the object and reference fields:

\[\tag{6}\Psi_H=\Psi_0+\Psi_R\]

and the irradiance of the field at the hologram is given by (assuming parallel polarization of the waves):

\[\tag{7}\begin{align}I_H&=\Psi_H\Psi_H^*=(\Psi_0+\Psi_R)(\Phi_0+\Phi_R)^*\\&=|\Psi_0|^2+|\Psi_R|^2+\Psi_0\Psi_R^*+\Psi_R\Psi^*_0\end{align}\]

After processing, and apart from a constant term, the transmittance \(\text{T}\) of the hologram is proportional to the irradiance of the field at the hologram;

\[\tag{8}T=K[|\Psi_0|^2+|\Psi_R|^2+\Psi_0\Psi^*_R+\Psi_R\Psi^*_0]\]

When illuminated by the reference wave, the field transmitted by the hologram \(\Psi_T\) is given by the hologram transmittance multiplied by the reference wave field: 

\[\tag{9}\Psi_t=K[\Psi_R(|\Psi_0|^2+|\Psi_R|^2)+|\Psi_R|^2\Psi_0+\Psi^2_R\Psi^*_0]\]

The first term in this equation for \(\Psi_T\) is simply the transmitted wave altered by an attenuation factor. The second term is the original object wave multiplied by an amplitude factor; this term represents the virtual holographic image of the object. The third term is the conjugate object wave.

In off-axis holography, the real image formed by this wave is weak, lies out of the field of view, and does not make a significant contribution to the imaging process.

However, for Gabor’s original in-line holography, this term represented an objectionable twin image which overlapped and obstructed viewing of the desired image.

An important contribution of the Leith and Upatnieks off-axis reference scheme was the elimination of this twin image. 

Many different types of holograms can be made by varying the location of the object relative to the recording medium, the directions and relative angles of the object and reference beams, and the wavefront curvature of these beams.

The properties of these hologram types vary greatly; much research has been performed to characterize and successfully apply the different formats. Vigorous work is still being pursued in both areas of imaging and technical applications.

 

 

3.  HOLOGRAPHIC INTERFEROMETRY

Interferometry provides a means of measuring optical path differences through the analysis of fringe patterns formed by the interference of coherent light waves. Optical path differences of interest may be produced by mechanical displacements, variations in the contour of one surface relative to another, and variations in the refractive index of a material volume.

Classical interferometry involves the interference of two relatively simple optical wavefronts which are formed and directed by optical components. These components must be of sufficient quality that they do not introduce random phase variations across the field that compete with or totally mask the optical path length differences of interest.

Typical examples of classical interferometry include the use of configurations such as the Michelson or Twyman Green and Mach-Zehnder interferometers to determine the surface figure of optical components, study the refractive index variation in optical materials, and visualize the properties of flowing gases. The need for high-quality optical surfaces in classical interferometry is a consequence of the difficulty, using classical optical methods, of generating two separate but identical optical wavefronts of arbitrary shape.

Although it was not immediately recognized by early holography researchers, the ability to holographically record then replay an arbitrary wavefront in a predictable fashion obviated this basic limitation of classical interferometry. With holographic interferometry, polished optical surfaces are not required and diffusely reflecting objects of any shape may be studied. 

In holographic interferometry, a wavefront is stored in the hologram and later compared interferometrically with another wavefront. Phase differences between these two wavefronts produce fringes that can be analyzed to yield a wide range of both qualitative and quantitative information about the system originating these two wavefronts.

Several researchers working independently made experimental observations related to this fact.

Once the full implication of this discovery was realized, a period of intense research activity began to develop a solid theoretical understanding of this powerful new technique. Holographic interferometry quickly became the most important application of the relatively young science of holography.

Although other branches of holography have successfully matured, most notably \(\text{HOEs}\), holographic interferometry remains today the area in which holography has probably made the greatest impact.

As stated earlier, holographic interferometry involves the interferometric comparison of two wavefronts separated in time. This comparison can be made in a variety of ways which constitute the basic methods of holographic interferometry: real-time, double-exposure, and time-average.

Real-time interferometry is realized by the interference of a holographically reconstructed object wave with the wave emanating from the actual object. This is accomplished as follows. The holographic plate is exposed, developed, then replaced in its holder in its original position. Reference- and object-beam intensities are adjusted so that the illuminated object and its holographic image are of approximately equal brightness.

Since the reconstructed object wavefront is \(180^\circ\) out of phase with the object wavefront, the object should be dark when viewed through the holographic plate.

In practice, one or two broad fringes usually appear across the object due to emulsion shrinkage effects and lack of complete mechanical precision in returning the holographic plate to its original position.

Any disturbance of the object which results in a mechanical displacement of its surface will now produce a fringe system which can be viewed in real time. The structure and periodicity of the fringes are related to the surface displacement.

The mechanical surface deformation can result from an applied force, change in pressure, change in temperature, or any combination of the three. The quantitative details of this surface deformation can be derived from an analysis of this fringe system.

In double-exposure holographic interferometry, the two wavefronts to be compared are stored in the same hologram. This is done by holographically recording the image of the object under study in two exposures separated in time in the same holographic plate.

If nothing is done to alter the object wavefront between these two exposures, the resulting image will appear as for a single-exposure hologram.

However, if the object is perturbed in some way between these two exposures, an interference fringe system will appear in the final image. Again, this fringe system is related to the mechanical deformations of the object surface caused by the disturbance.

Real-time holographic interferometry allows one to study the effects of object perturbation of varying types and degrees over any desired length of time and in real time. In contrast, double-exposure holographic interferometry examines a particular change of the state of the object between two particular points in time. A double-exposure holographic interferogram then might be thought of as a single data point record.

The interferogram might be a record of the change of the object from one stable state to another, which might be recorded with a continuous wave laser. Or the interest might be to compare two states of a rapidly varying system most effectively recorded using a pulsed laser.

In some respects, the double-exposure holographic interferogram involves less experimental complexity, because both exposures are made in a single hologram plate held in a fixed position.

Mechanical registration of the plate to a baseline position is not required . Emulsion shrinkage due to wet process development of silver halide film affects the holographic fringe systems for both exposures in the same way; therefore, it is not a problem for double-exposure interferometry.

Another feature which may or may not be of benefit, depending on the parameters of the experiment, is that the superimposed images for the two exposures are in phase, thereby producing a bright baseline image. Double-exposure interferometry has been used very effectively to record fast events such as the flight of a bullet passing through a chamber.

The first exposure is made of the chamber alone before passage of the bullet; the second exposure is made with the bullet in midflight. The interferogram is an interference recording of the refractive index variations in the chamber created by the disturbance of the bullet.

Vibrating surfaces may be studied using either real-time or time-average holographic interferometry. A vibrating object presents a continuum of surface configurations or surface deformations to an interferometric system. A unique interferometric fringe system is associated with each state of the surface for any particular point in time during the vibrating cycle.

In real-time interferometry, the interference fringes are formed by the addition of wavefronts from the surface of the object at rest and from the vibrating surface at some point during its vibrating cycle. The fringe pattern observed is a visual time average of this continuum set of interferogram fringe systems. A time-average holographic interferogram is made by exposing the holographic plate while the object is vibrating; the exposure time is usually multiple vibration periods.

This hologram may be thought of as a continuum set of exposures, each recording the interference of the object wave with its temporal counterparts in the rest of the continuum over one cycle. The end result is a fringe pattern, directly related to the surface vibration pattern, in which the fringe lines represent contours of constant vibration amplitude.

A more physical view of the process derives from observing that holographic fringe movement in the recording medium due to object movement nullifies the holographic recording.

Thus, regions of a vibrating surface in motion (antinodes) will appear dark while regions at rest (nodes) will appear bright.

Stroboscopic illumination has long been used to study objects in motion. Coupling this technique with holographic interferometry produces interferograms of vibrating objects with enhanced fringe visibility and greater information content.

The technique may be used to make real-time observations or to record double-exposure holograms of vibrating surfaces. In the real-time configuration, the hologram of the test object at rest is made in the usual fashion. The object is then vibrated and strobed with a laser set to flash at a particular point in the vibrating cycle.

The fringe system formed is produced by interference of the wavefront from the object at rest and the wavefront from the object at this particular point in the cycle. The timing of the laser flash may be varied to observe the evolution of the surface vibration throughout its entire cycle. A double-exposure interferogram is formed by exposing the hologram plate to two flashes from the strobed laser.

In this manner, any two states of the vibrating surface may be compared during its cycle by varying the timing of the laser flashes and their separation. The actual exposure may extend over several vibration cycles. This method results in fringes of much higher contrast than those yielded by time-average holography.

An interesting variant of hologram interferometry is contour generation. This is accomplished by making two exposures of an object with a refractive index change in the medium surrounding the object or a change in the laser wavelength between exposures. Either method yields fringes on the surface of the object.

The fringe positions are related to the height of points on the object relative to a fixed plane. The two-wavelength method may be implemented in real-time by first making a hologram of an object in the usual manner at one wavelength, then illuminating both the object and the processed hologram (carefully placed in its original position) at a different wavelength. Both methods have been successfully applied in a variety of situations.

In many cases, the interpretation of the fringe pattern produced by a holographic interferogram is a simple matter of qualitative assessment. For example, defects or flaws may be identified by anomalous local variations in a background fringe pattern. The presence or absence of these anomalies may provide all the information required in a nondestructive evaluation experiment.

However, a detailed quantitative assessment of the mechanical deformation of the surface may be desired—this can involve a complex mathematical analysis of the fringe system. Quantitative analysis of the fringe pattern is often complicated by the fact that the fringes are not necessarily localized on the surface of the object. The interpretation of holographic interferograms and analysis of the fringe data have been the subject of considerable study.

Numerous methods such as sandwich holographic interferometry, fringe linearization interferometry, difference holographic interferometry, and fringe carrier techniques have been developed to facilitate this interpretation.

In addition, the development of automatic fringe reading systems and data reduction software have greatly aided this process. However, fringe data reduction remains a challenge for many situations despite the progress that has been made.

The basic methods of holographic interferometry (real-time, double-exposure, and time-average) are in widespread use and continue to be the mainstay of this technique.

However, important refinements have been made in recent years which have greatly added to the power of holographic interferometry. These advances include the use of real-time recording media, and heterodyne holographic interferometry Real-time holographic recording materials (such as photorefractive crystals) provide an adaptive feature that makes the interferometer less sensitive to vibration air currents, and other instabilities.

The reliability of the interferometric process in a hostile environment is thus improved. Heterodyne techniques using two separate reference waves and a frequency shift between these two waves upon reconstruction has greatly improved the accuracy of holographic interferometry.

Measurements with accuracies as high as \(\lambda/1000\) can be made using heterodyne methods. Holographic moire, infrared holographic interferometry, and the use of optical fibers have also significantly extended the capabilities of holographic interferometry.

In the laboratory, where conditions are well-controlled, silver halide film has been the recording material of choice for holographic interferometry due to its relatively high

 

 

 

sensitivity, low cost, and reliability.

However, in field applications such as the factory floor, the wet processing requirements of silver halide film make this material much less attractive and, for some time, inhibited the use of holographic interferometry in many situations.

Other materials that do not require wet processing (such as photopolymer films) are available, but these materials have very low sensitivity. The development of the thermoplastic recording material, which does not require wet processing but retains the high sensitivity of silver halide film, made possible the much more convenient application of holographic interferometry in industrial situations.

Several companies (Newport, Rottenkolber, and Micraudel) have commercially marketed holocamera systems using this material. The Rottenkolber and Micraudel systems are film-based with supply and take-up rollers.

Only one exposure may be made on each area of film. The Newport holocamera has a smaller recording area than the film-based systems, but the plate may be erased and reused for several hundred exposures. A holographic interferogram made using the Newport holocamera is shown in Fig. 2.

Holographic interferometry has been applied to an enormous range of problems; this is a simple testimony to its utility and versatility. The classical interferometric testing of the figure of optical components during fabrication can be augmented with holographic interferometry to test for figure during the grinding process since the surface of the test object does not need to be polished.

The ability of holographic interferometry to make precise measurements of very small mechanical displacements has enabled it to be used in stress-strain measurements in materials, components, and systems. Mechanical displacements observed with holographic interferometry are often the result of thermal disturbances. Measurement of these thermally induced mechanical displacements with holographic interferometry can provide an accurate determination of the heat transfer properties of the material or system under study.

Similarly, diffusion coefficients in liquids can be determined using holographic interferometry. Flow visualization and the accurate determination of fluid-flow properties using holographic interferometry has been an intense area of study.

As noted earlier, the technique can also be used to study high-speed events using short-pulse lasers in the double-pulse mode. Vibration analysis is 

 

 

one of the more powerful applications of holographic interferometry.

In this area, the technique has been applied to a diverse array of problems including studies of the vibration properties of musical instruments, vibration patterns in the human eardrum, and vibration properties of mechanical parts such as turbine blades. The application of holographic interferometry to turbine blade mechanics is illustrated in Fig. 3.

One of the great virtues of holographic interferometry is that a tremendous wealth of information can be garnered from its application without destroying the test object or system. As a result, nondestructive evaluation or nondestructive testing has been one of the most important areas of application for this technique. As an example, holographic interferometry has been successfully used to observe subsurface defects in solid opaque objects.

Even though the interference pattern is produced strictly by mechanical surface deformations, these surface variations are often indicative of subsurface changes (e. g., ply separations in automobile tires and interlayer delamination in composite materials).

Subsurface defects are usually manifest in local anomalies of the fringe pattern and a qualitative examination of the interferogram will often discern the effect. The literature is replete with articles describing these and many other applications of holographic interferometry.

For the reader interested in an in-depth discussion of the theory and application of holographic interferometry, numerous textbooks and review articles are available.

 

Electronic Holography

Even with the use of thermoplastic recording media, holographic interferometry remains a challenging and, in many cases, unacceptable technique for industrial applications—particularly those that involve on-line quality testing in a production environment.

Speckle-pattern interferometry, another technique closely associated with holographic interferometry, alleviates many shortcomings of the traditional holographic approach when combined with electronic image recording and processing equipment.

Speckle is the coarse granular or mottled intensity pattern observed when a dif fuse surface is illuminated with coherent light. Wavelets reflected from the randomly oriented facets of an optically rough surface interfere to produce this effect when the size of the facets is on the order of a wavelength or larger.

Although this interference occurs throughout the space occupied by the wave scattered by the surface, the interference that produces the observable pattern takes place in the plane of the detector or recording medium (i. e., the retina of the eye or the film plane of a camera).

The speckle-pattern recorded by an imaging system (eye or camera) is known as subjective speckle, while the intensity variation detected by a scanning detector above a coherently illuminated diffuse surface is referred to as objective speckle.

Objective speckle is the resultant sum of the waves scattered from all parts of the surface to a point in space; in subjective speckle, wave summation in the observation plane is limited to the resolution cell of the system. The objective-speckle scale depends only on the plane in space where it is viewed, not on the image system used to view it.

The size of the image plane or subjective speckle depends on the aperture of the viewing or imaging system. For subjective speckle, the characteristic speckle diameter, \(d_{sp}\) is given by

\[\tag{10}d_{sp}\approx\frac{2.4\lambda v}{a}\] 

where \(\lambda\) is the wavelength, \(v\) is the distance from the lens to the image plane, and \(a\) is the diameter of the viewing lens aperture.

A fringe pattern is formed when the speckle patterns of the diffuse surface in its original and displaced positions are properly combined. The formation of this fringe pattern is known as speckle-pattern interferometry, of which there are two basic types: speckle pattern photography and speckle-pattern correlation interferometry. Both techniques, which form the basis for electronic speckle-pattern interferometry \(\text{(ESPI)}\), and other forms of electronic holography will be discussed in this section.  

By varying the recording and viewing configurations, speckle-pattern interference fringes can be made sensitive to in-plane and out-of-plane displacements, displacement gradients, and the first derivative of displacement gradients.

Speckle-pattern interferometry has two distinct advantages over holographic interferometry: (1) the direction of the magnitude sensitivity of the fringes can be varied over a larger range, and (2) the resolution of the recording medium for speckle-pattern interferometry does not need to be nearly as high.

Therefore, speckle-pattern interferometry is a much more flexible technique, although the fringe definition is not nearly as good as with holographic interferometry due to the degradation of the images by the speckle pattern.

In speckle-pattern photography, the object is illuminated by a single light beam; no reference beam is involved. Some of the light scattered by the object is collected by a lens and recorded on photographic film.

The film plane may be an image plane (in-focus) or some other plane (out-of-focus). The location of the film plane determines whether the resulting interferometric fringes are sensitive to in-plane or out-of-plane motion.

Two exposures of the film are made: one with the object in its original position, the second with the object deformed or displaced. Proper illumination of the film negative with coherent light produces a fringe pattern in the observation plane which is related to the object motion. With the use of appropriate recording and viewing geometries, the fringes may be made to superimpose an image of the object.

If the object is illuminated by a plane wavefront and the film is in the focal plane of a lens, the fringes are related to out-of-plane displacement gradients. Illumination of the object by a diverging wavefront in the proper geometry yields fringes related to the tilt of the object.

Speckle-pattern photography can be used to make time-average stroboscopic and double-pulse measurements just as in holographic interferometry. In speckle-pattern correlation interferometry, a reference beam (either specular or diffuse) is incident upon the observation or recording plane in addition to the light scattered by the object.

Interferometric fringes are produced by the correlation of the speckle patterns in the observation plane for the displaced and undisplaced object. Real-time or live-correlation fringes may be produced as follows. The object and reference beams are recorded with the object in its original position using photographic film. The film is developed and the film negative is replaced in its original position.

The negative is illuminated with object and reference light, and the object is displaced. Correlation fringes are produced by the process of intensity multiplication.

Because of the contrast reversal of the film negative, minimum transmission is found in areas of maximum correlation between the pattern recorded and the pattern produced by the displaced object.

Unfortunately, the correlation fringes produced using this technique are of low contrast.

The variation in the correlation of the two speckle patterns which produces the fringes may be made sensitive to different components of surface displacement by using different object and reference beam geometries. One of the most important configurations uses a specular in-line reference beam introduced with a beam splitter or mirror with a pin hole.

This configuration may be used to make dynamic displacement measurements or to observe the behavior of vibrating objects in real time. This particular optical geometry is also the most popular arrangement for \(\text{ESPI}\).

In \(\text{ESPI}\), the photographic film processing methods used for speckle-pattern photography and speckle-pattern correlation interferometry are replaced by video recording and display technology. The concept of using video equipment for this purpose was originated by several researchers working independently during the same period.

For speckle pattern interferometry , the minimum speckle size is usually in the range of 5 to 100 \(\mu m\) so that standard television \(\text{(TV)}\) cameras can be used to record the pattern. The main advantage of using \(\text{TV}\) equipment is the high data rate. Real-time correlation fringes may be produced and displayed on the \(\text{TV}\) monitor at 30 frames per second.

In addition, the full array of modern video image processing technology is available to further manipulate the image once it is recorded and stored in the system.

Another advantage is the relatively high light sensitivity of \(\text{TV}\) cameras which operate at low light levels, thus enabling satisfactory \(\text{ESPI}\) measurements with relatively low power lasers.

The ready availability of advanced video recording and processing equipment, its ease of use, and its flexible adaption to various applications make \(\text{ESPI}\) a near-ideal measurement system in many instances—particularly, industrial situations (such as an assembly line) where rapid data generation and retrieval, and high throughput are required.

\(\text{ESPI}\) overcomes many of the objections of holographic interferometry and has been used extensively for industrial measurements in recent years.

Intensity correlation fringes in \(\text{ESPI}\) are produced by a process of video subtraction or addition. In the subtraction process, the image of a displaced object is subtracted from an electronically stored image of the object in its original position to produce the correlation fringes.

To observe these fringes, the subtracted video signal is rectified and high-pass filtered, then displayed on a video monitor. This video processing is analogous to the reconstruction step in holography.

For the addition method, both original and displaced images are added optically at the photo cathode of the \(\text{TV}\) camera. The \(\text{TV}\) camera detects the light intensity and, again, the signal is full-wave rectified, high-pass filtered , and displayed on the \(\text{TV}\) monitor.

Because of the persistence of the \(\text{TV}\) tube, the two images need not be recorded simultaneously; however, they must be presented to the camera within its persistence time, usually on the order of 100 ms. The various optical configurations used in speckle-pattern correlation interferometry, employing both specular and diffuse reference beams, may be used in \(\text{ESPI}\) as well.

The most popular of these configurations uses a specular in-line reference beam and may be used to make real-time vibration studies. \(\text{ESPI}\) has been used for this purpose

 

 

more than any other application. This optical configuration is shown in Fig. 4. The object and reference beams in Fig. 4 are derived from the same laser with the use of a beam splitter, not shown for simplicity. In holographic interferometry, a high-resolution film is used and the reference beam angle may be any practical value desired.

In \(\text{ESPI}\), the recording medium \(\text{(TV}\) camera) has a resolution two orders of magnitude lower than holographic film (on the order of 30 line-pairs per millimeter). Therefore, in \(\text{ESPI}\), an in-line reference beam must be used.

Furthermore, the aperture of the system must be small enough to keep the interference angle below one degree.

All the usual modes of holographic interferometry (real-time , time-average , stroboscopic, and double-exposure) may be performed with \(\text{ESPI}\). A time-average \(\text{ESPI}\) interferogram of an object made with the system operating in the subtraction mode is shown in Fig. 5a. For comparison, a holographic interferogram of the same object is shown in Fig. 5b.

\(\text{ESPI}\) has been applied to a wide range of measurement problems. These applications are discussed in numerous books, technical papers, and review articles. 

Despite the flexibility of \(\text{ESPI}\) and its ease of use, fringe definition is poor compared to holographic interferometry—this has somewhat limited its use. Speckle-averaging and video-processing techniques have provided some improvement in interferogram quality, but very fine interference fringes are still difficult to discern with \(\text{ESPI}\).

A significant improvement in interferogram quality has been achieved with a newer technique: electro-optic holography \(\text{(EOH)}\).This technique uses the same speckle interferometer optical configuration as \(\text{ESPI}\), but processes the video images in a different manner.

In \(\text{EOH}\), a phase-stepping mirror is added to the reference leg to advance the phase of the reference beam by \(90^\circ\) between successive video frames. Subsequent processing of these phase-stepped images combined with frame and speckle averaging provides interferograms in real-time with nearly the same resolution and clarity of the traditional film-based holographic interferogram. An interferogram made with an \(\text{EOH}\) system is shown in Fig. 6.

 

 

4.  HOLOGRAPHIC OPTICAL ELEMENTS

An optical element with the power to direct and/or focus a light wave can be made by recording the fringe pattern formed by two interfering light beams. \(\text{HOEs}\) or diffractive optical elements, thus produced, have several features that distinguish them from 

 

 

conventional optics. A compilation of articles on diffractive optics. 

Different types of elements may be produced by varying the curvature of the interfering wavefronts, interbeam angle, and configuration of the recording surface. Lenses with mild or very strong focusing power and plane or focusing mirrors are easily produced.

The recording substrate may be plane or any arbitrarily curved shape. An element combining 

 

 

diffractive power with refractive power can be made by placing the recording medium on a curved surface. This method may be used to reduce the aberration of the combined optic since the achromatic dispersion of diffraction and refraction are of opposite sign.

Although any of the many types of holographic recording materials may be used to make an \(\text{HOE}\), dichromated gelatin and photoresist are preferred because of their high resolution and extremely low optical scatter. Dichromated gelatin has the additional advantage of forming \(\text{HOEs}\) of very high diffraction efficiency.

Photoresist forms a surface relief hologram which makes possible the economical mass production of \(\text{HOEs}\) with straightforward mechanical replication means. Since the power of an \(\text{HOE}\) is derived from diffraction at the element’s surface, the \(\text{HOE}\) may be very thin and lightweight.

\(\text{HOEs}\) may be produced by the direct interference of physical light waves, or by calculating the desired interference pattern and printing this pattern onto a substrate by either photographic or electron beam lithographic means.

Computer-generated \(\text{HOEs}\) are advantageous when the required optical wavefronts are difficult to create physically. 

The use of the term ‘‘holographic optics’’ is not technically correct because the definition of holography implies that at least one of the wavefronts being combined to produce an interference record is an information carrier.

Consequently, the term ‘‘diffractive optics’’ is gaining popularity and, when applied to gratings, the term ‘‘interference gratings’’ is certainly more appropriate.

In this brief discussion, however, we will continue to use the currently popular ‘‘holographic’’ terminology.

Certainly one of the most common and successful applications of holographic optics is as a grating in spectrographic instruments. The main advantage of holographic gratings are that they can be made free of the random and periodic groove variation found in even the finest-ruled gratings, and they have low light scatter.

This latter property is especially important when even a small amount of stray light is objectionable (such as in the study of Raman spectra of solid samples).

To produce high-quality holographic gratings , extreme care must be used in the fabrication process. Photoresist is the preferred recording material for reasons mentioned above; however, it is very insensitive and requires long exposure times, often many hours.

Therefore, a highly stable optical system is essential. The recording room must be free of air currents , the air must be filtered and dust-free, and the photoresist coating must be defect-free. Stray light scatter from optical mounts and other objects in the recording setup must be eliminated by proper baffling and masking.

The interfering beams must be appropriately conditioned by spatial filtering to ensure diffraction-limited performance. If beam-forming optics are used, for example, to produce collimated beams for making plane holographic gratings, these optics must be aberration-free and of diffraction-limited quality.

After exposure and chemical development, the surface relief pattern is metalized and the holographic grating is replicated as conventional master-ruled gratings are replicated.

Both positive and negative photoresists are available for making holographic gratings, however, the negative resist is seldom used.

Grating-diffraction efficiency in the various orders is determined by the groove profile.

In a ruled grating, the groove is profiled by appropriately shaping the diamond tool. Holographic gratings have a sinusoidal profile; blazing, in this case, is accomplished by ion etching.

A wide range of groove spacing is possible with ruled gratings, however, holographic gratings offer more flexibility with respect to the groove pattern. For example, groove curvature may be used in holographic gratings to reduce aberrations in the spectrum, thereby improving the throughput and resolution of imaging spectrometers.

The grooves in ruled gratings are produced by the traveling diamond tool, one after another. In holographic gratings, all grooves are produced in parallel; thus, the fabrication time for holographic gratings can be considerably shorter.

Another important instrumental \(\text{HOE}\) application is in optical beam scanning; the most common example of this is the supermarket scanner. Laser beam scanning is usually accomplished by either mechanical means (e.g., rotating mirror) or with the use of some transparent medium whose optical properties are changed by some sort of stimulation (e.g., acousto-optic cell).

Holographic scanners offer advantages over both of these more conventional methods.

The working principle of the holographic scanner may be illustrated by considering the translation of a focusing lens through an unexpanded laser beam. As the beam intercepts the lens from one side to the other, it is simultaneously deflected and focused at the lens focal point on the lens axis.

Thus, moving the lens back and forth causes the laser beam to sweep back and forth in the focal plane of the lens. In its basic form, a holographic scanner is simply an \(\text{HOE}\) lens or mirror translating through the scan beam. The principal advantage of the holographic scanner over conventional scanning means is the ability to combine beam deflection and focusing into a single element.

The form of both the deflection and focusing function can be tailored in a very flexible way by proper design of the \(\text{HOE}\) formation optical system. For example, the scan element may be easily made a line segment rather than a focal spot, and the locus of the scanned focal spot or line may be placed on either plane or curved surfaces. Multiple scan beams with multiple focal points may be generated by a scanner in the form of a segmented rotating disk.

Each segment or facet of this disk has different deflection and focal properties. As the disk rotates through the beam, a multiplicity of scan beams is produced which can densely fill the desired scanned volume. This feature is especially important in a supermarket application because it allows products of varying sizes and shapes to be rapidly scanned.

A further advantage of the \(\text{HOE}\) scanner is that the scanner disk can be small, thin, and lightweight, thereby greatly reducing the demands on the drive system. The disk format also produces little air movement due to windage and is very quiet in operation.

In addition to serving as the beam deflector, the holographic scanner also collects the light scattered from the laser spot on the product and directs it to the optical detector.

This scattered light illuminates the holographic scanner along the conjugate object beam path and is diffracted into the fixed conjugate reference or primary scan beam path where it is

 

 

accessed by a beam splitter. The light scattered from all points in the scan volume is thus directed to a single, fixed detector position.

An optical schematic for a point-of-sales scanner is shown in Fig. 7.

The ability to combine several optical functions into a single \(\text{HOE}\) makes this device attractive in many situations. Significant savings in space, weight, and cost can often be realized by replacing several conventional elements with a single \(\text{HOE}\) device.

This feature has been incorporated into an optical head for compact disk applications with the use of a multifunctional \(\text{HOE}\).

An optical diagram of the device is shown in Fig. 8. The objective lens images the light-emitting point of the laser diode \(\text{(LD)}\) to the compact disk. The light scattered from this focal point on the disk is reimaged by the objective lens through the \(\text{HOE}\) to the photodetector \(\text{(PD)}\).

In this application, the \(\text{HOE}\) serves as a spherical lens, beam splitter, aberration-correcting lens, and cylindrical lens. In addition to simplifying the optical system, the \(\text{HOE}\) provides a better means of aligning the optical system. 

Holography has even been applied to one of the oldest instrumental functions known— 

 

 

the keeping of time. This has been accomplished by using an \(\text{HOE}\) as a holographic sundial. 

 

 

5.  HOLOGRAPHIC INSPECTION 

Quality assurance inspection and testing, important functions in any industrial manufacturing process, have also benefited from advances in holography. Holographic methods have been applied to the quality control problem in several areas, such as identifying and locating subsurface mechanical defects and determining the presence or absence of certain surface features.

Holographic interferometry has been successfully applied to some of these problems, and optical processing methods have also yielded good results in many cases.

Matched and spatial filtering in the Fourier transform plane of an optical processing system have proved to be especially powerful means of identifying features and determining surface detail.

In this section, we describe a unique combination of holography and classical optical processing methods that made possible a very successful means of rapidly detecting defects in devices with highly regular and repetitive patterns. 

Defects in integrated circuit photomasks and wafers at various stages of processing can greatly diminish the final device yield. Since the economics of wafer production is strongly influenced by yield, there has been an ever-present incentive to increase this yield by minimizing the number of defects introduced at various points in the production process.

One way to increase yield is to identify these defects early, and eliminate them before they cascade in a multiplicative manner through the various stages of the process.

For years, the inspection of integrated circuit photomasks and wafers was performed by either manual microscopic examination or automated serial scanning using an optical detector. The latter method involves comparison of the detector signal from a magnified portion of the test pattern to a similar portion of a reference pattern, adjacent pattern, or digital design database.

In either case, the inspection process was long and tedious, often requiring many hours or days to inspect a single photomask or wafer. These methods are very slow because of the large number of pixels involved and the serial pixel-by-pixel nature of the inspection.

Clearly, a great advantage would be afforded by the ability to examine all the pixels in parallel rather than serial format. 

This observation prompted a number of researchers to consider optical processing methods for integrated circuit inspection and for addressing other types of problems involving highly repetitive patterns such as cathode-ray tube masks and \(\text{TV}\) camera tube array targets.

The concept in all cases was to eliminate perfect pattern information and highlight defect areas of the image by spatial filtering in the Fourier transform plane. These methods met with only limited success because of the difficulty in fashioning effective blocking filters and the need for extremely high quality, large-aperture, low F-number Fourier transform lenses.

Despite considerable work in this area, none of these efforts resulted in the development, production, and in-process use of integrated circuit inspection systems using Fourier optical processing concepts.

This situation was reversed by the adaption of a holographic documentation system used to document the surface microstructure of high-energy laser optical component test samples.

A schematic diagram of the holographic documentation optical system is shown in Fig. 9. An \(\text{F}/ 3.42\) lens was used to image the test target onto the hologram film and an argon laser operating at a wavelength of 514.5 nm was the illumination source.

A polarizing beam-splitting cube and a half-wave plate were used to split the beam into object and reference beams, and to adjust the beam ratios. A second polarizing beam-splitting cube and quarter-wave plate were used to efficiently illuminate the test target and direct the reflected light to the holographic plate.

The holographic image was reconstructed with the conjugate reference beam by removing mirror M-4. The test target was removed and the holographic image of the sample was examined with the aid of a

 

 

microscope. The calculated resolution of this system (classic Rayleigh resolution limit) was 4.0-\(\mu m\). A photograph of the holographic reconstruction of the standard Air Force resolution target made with this system is shown in Fig. 10. The smallest bars in this target are on 4.4-\(\mu m\) centers.

Thus, the resolution observed with this system was comparable to the calculated value. 

In considering how the documentation system might be adapted to other applications (including the integrated circuit inspection problem), Fusek et al. observed that because the real image of the test target was being examined by conjugate reconstruction, both functions of the classic Fourier optical system (i.e., transform and inverse transform) were performed in the documentation system.

Because of reverse ray tracing, a high-quality matched pair of specially designed Fourier transform lenses is no longer required to produce a diffraction-limited output image.

As with previous work, the objective was to attenuate the image area where the pattern is defect-free and highlight the defects. This is done simply by placing the appropriate blocking filter in the Fourier transform plane. The method works effectively only if the filter efficiently blocks the light associated with defect-free areas of the image and efficiently transmits the defect light.

Fortunately, this is the case for integrated circuit masks and wafers which consist of regular patterns of circuit elements repeated many times over the area of the wafer. For such patterns, the intensity distribution in the Fourier transform plane is a series of sharp spikes or bright points of light.

Low spatial frequencies associated with slowly varying features (such as line-spacing) are represented by light points near the optical axis of the imaging lens. High spatial frequencies, representing such features as edge and corner detail, lie farther out in the Fourier transform plane.

The Fourier transform plane intensity pattern for a production-integrated circuit photomask is shown in Fig.11. Since defects are usually of a nonregular

 

 

 

 

nature, the light associated with defects is generally spread out fairly uniformly over the Fourier transform plane.

Thus, a filter designed to block the regular-pattern light passes most of the light associated with defects. 

The most straightforward way to produce the blocking filter is by photographic means, with the film placed in the Fourier transform plane. The filter is made first, then the hologram is exposed with the object beam passing through this filter. Thus, the reconstructed wave that produces the output image is effectively filtered twice.

A problem with this method of filter fabrication is the extremely large range of intensities in the Fourier transform plane which can cover as many as ten orders of magnitude. If the filter is properly exposed near the axis where the transform light is brightest, high-spatial-frequency components away from the axis will be underexposed and inadequately filtered.

However, if high frequencies are properly exposed , low frequencies will be overexposed, and too much defect light will be filtered. An effective means of alleviating this intensity-range problem is dynamic range compression by multistep filter generation.

The process is as follows. With a mask in place, a holographic plate is exposed to the Fourier transform pattern with exposure parameters set to record the intensity distribution in the low-frequency region near the optical axis. After processing, this plate (Stage 1 filter) is replaced in the Fourier transform plane and a hologram of the mask is made through this filter.

The hologram is illuminated by the conjugate reference beam and a second filter plate (Stage 2 filter) is exposed to the resulting Fourier transform intensity pattern. This pattern now has its low-frequency components attenuated because of the action of the Stage 1 filter. The Stage 2 filter can now be used to record a Stage 3 filter. The process may be repeated as many times as necessary to produce a filter with the desired attenuation properties.

Because the defect light is of much lower intensity in the Fourier transform plane than the light corresponding to nondefect areas, defect light does not contribute significantly to the exposure of the filter, and the object under test (containing defects) may be used to generate the filter. Stage 1 and 2 filters for a defect calibration test mask (Master Images \(\text{VeriMask}^\text{TM}\)) are shown in Fig.12. 

Performance of the breadboard documentation system using the \(\text{VeriMask}^\text{TM}\) is shown in Fig.13. Figure 13 a is a photo of a magnified region of the \(\text{VeriMask}^\text{TM}\) containing a pinhole defect. Figure 13 b shows the Stage 2 filter image of this same defect which is clearly enhanced.

In addition, dimensional variations in the mask pattern from die to die are also highlighted.

The breadboard holographic inspection technology developed by Fusek and coworkers was further advanced and placed into production by Insystems of San Jose, California. 

This company produced a series of mask and wafer inspection machines based on the holographic optical processing technique. The optical configuration of the Insystems Model 8800 Wafer Inspection System is shown in Fig. 14. The commercial instrument uses an argon ion laser as the light source, and the system functions in an optical manner identical to that of the original breadboard device.

However, many refinements were incorporated into the commercial system which yielded substantially improved performance over the breadboard system. These refinements, which included a sophisticated Fourier transform lens design, made possible adequate performance without using the multistep filter generation technique.

The wafer test piece and the hologram are placed on a rotating stage under a microscope and a video camera so that the filtered image of the defect and the microscopic image of the defect on the actual wafer can be viewed simultaneously. Figure 15 illustrates the advanced filtering capability of the commercial instrument. This instrument is sensitive to defects as small as \(0.35\mu m\)

Disadvantages of the holographic defect detection system are the inconvenience and time delays associated with the wet processing of the silver halide holographic recording material. The use of photorefractive crystals, which operate in real time and do not require wet processing, has been studied as a means of eliminating these disadvantages. The dual functions of image recording and spatial filtering are combined by placing the crystal in

 

 

the Fourier transform plane and adjusting the reference beam intensity to the level of the defect light intensity. Since the light in the Fourier transform plane associated with defects is much lower in intensity than nondefect light, only the defects will be recorded with high diffraction efficiency.

Practical use of photorefractive crystals in this application has not been realized, however, because these crystals have relatively low sensitivity and are not available in large sizes with good optical quality. 

 

 

 

 

6.  HOLOGRAPHIC LITHOGRAPHY 

The lithographic transfer of an integrated circuit photomask pattern to a resist-coated integrated circuit wafer has been accomplished by several methods, including contact printing, proximity printing, and step-and-repeat imaging.

Each method has advantages and disadvantages. Contact printing is a simple, straightforward method suitable for 

 

 

printing large wafer areas, but damage to the mask and contamination of the wafer are common problems. Proximity printing is resolution-limited because of near-field dif fraction.

The diffraction problem can be eliminated by imaging the mask onto the wafer, but full-field imaging systems do not provide the resolution required over the full area of the wafer. Stepper systems, which image only a small area of the mask at a time, provide the required resolution; however, they are complex and expensive because of the resolution demands placed on the optical imaging system and the mechanical difficulty in accurately stitching together the multiple image patterns over the full area of the wafer. 

 

 

 

 

 

Clearly, a full-field method of printing the image onto the full area of the wafer with the required resolution is desirable. A holographic system capable of accomplishing this task has been developed by Holtronic Technologies Limited. Rather than using a lens system to image the mask on to the wafer, the Holtronic holographic system uses real-image projection by conjugate illumination to overlay the mask image onto the wafer.

Near-field holography is used to record the mask image by placing the mask in close proximity to the recording medium (100-\(\mu m\)  separation) and illuminating the mask from the back with a collimated laser beam (364-nm line from an argon ion laser).

To allow the introduction of an off-axis reference beam, an image of the mask could be relayed to the hologram plane with a lens. The approach taken was to eliminate the need for this lens with the use of the total internal reflection holography scheme of Stetson.

A diagram illustrating the optical principle is shown in Fig. 16. 

Light transmitted and diffracted by the mask is incident directly on the holographic recording material which is deposited onto the opposing surface of a prism. Reference light is introduced through the diagonal surface of the prism and reflected at the holographic coating/air interface by total internal reflection.

The recording medium is Dupont photopolymer. The holographic exposure is made with an expanded reference beam illuminating the entire hologram area.

Since three beams pass through the photosensitive material, three gratings are formed: (1) a reflection grating formed by the incident and reflected reference beams, (2) a reflection grating formed by the object beam and the incident reference beam, and (3) a transmission grating formed by the object beam and the reflected reference beam.

To reconstruct the mask wavefront, an illumination beam conjugate to the reflected reference beam is introduced through the prism. This incident illumination beam interacts with the transmission object grating to form the conjugate real image of the mask. The totally internally reflected and the Lippmann-reflected illumination beams interact with the reflection object grating to reinforce the mask image. 

During reconstruction and exposure of the photoresist-coated wafer, a small-area illumination beam is scanned over the hologram surface. Dynamic focusing of this scanned exposure beam eliminates the requirement that the mask and wafer substrates be ultraflat.

 

 

Figure 17 illustrates the 0.3-\(\mu m\) resolving capability of the holographic lithography process in 0.3-mm thick resist. The lines shown were printed on a silicon wafer coated with Olin Hunt \(\text{HPR}\) 204 i-line photoresist and developed using the Hunt \(\text{HPRD}\) 429 developer. The effective numerical aperture of the system is greater than 0.7.

 

 

7.  HOLOGRAPHIC MEMORY 

The information storage capability of holograms has been the subject of considerable study over the years with several applications in mind. With the parallel information storage and processing capability of holograms, and the promise of shorter access times, computer memory has received particular attention. Two review articles provide good summaries of this field of research through 1990. 

However, little mention is made of the work of Russian scientists who have also been very active in this field.

Of all the holographic material recording possibilities available, volume storage in photorefractive crystals has received the most attention. There are two main reasons for this emphasis: (1) the large information storage capacity of these crystals, and (2) their capability to meet the write-read-erase requirement in real time with no wet-chemical or other material-processing delays.

However, no commercial memory systems using holographic storage have been developed. One reason for this is the relatively large volume of space occupied by the laser beam-steering equipment and other optical components required in such a system, even though the actual holographic storage element may occupy a volume of less than a few cubic centimeters.

However, the primary reason is the limitations of the recording material. Despite their distinct advantages over other recording material candidates, photorefractive crystals have some significant limitations. It is difficult to grow large crystals with good optical quality and to achieve stable, long-term storage without destructive readout.

Recent work by Redfield and Hesselink shows promise for overcoming these previous limitations and leading the way to a practical holographic memory system.

Rather than concentrating on developing large, high-quality crystals, their approach is to form a large-volume memory element by using an array of small crystallites of strontium barium niobate in the form of small cubes or crystalline fibers.

Techniques have also been developed for accessing the holographic information stored in these crystallites without destructive readout.

Information is stored in the memory structure by recording Fourier holograms of checkerboard patterns (pages) of digital information. Access times are projected to be 100 to 1000 times faster than with conventional magnetic disk drives.