Light-in-flight digital holography display

In 1978 Abramson1 demonstrated a method called light-in-flight holography to display the locus of the zero optical path difference (OPD) between the object and the reference beams of a holographic setup. He used the short coherence length of an argon ion laser without an intracavity étalon. A picosecond laser was also used for this purpose.2 A similar method had been proposed by Boden et al.3 and Denisyuk et al.4 On the other hand, digital speckle pattern interfer ometry (DSPI) has developed as a powerful tool to perform several operations usually associated with holographic interferometry in the image plane; thus this method is also called digital holography. Defor mation measurements and generation of contours of three-dimensional objects are some examples.5*6 A review of some of these applications can be found in Ref. 7, but a profusion of recent developments exists in the literature. In its basic form the image of an object with a superposed coherent background is registered by a TV camera and then digitized and stored in a frame memory. Subsequent images are subtracted from the initial image, and the square or the modulus of the difference is shown on a monitor. A phase change between the reference and the object waves is introduced between the first and the final observed states. It can be produced, for example, by a deforma tion of the object or by a change in the illumination conditions. If this phase difference on the image is slowly varying on areas comprising several pixels,

In 1978 Abramson1 demonstrated a method called light-in-flight holography to display the locus of the zero optical path difference (OPD) between the object and the reference beams of a holographic setup.He used the short coherence length of an argon ion laser without an intracavity étalon.A picosecond laser was also used for this purpose.2A similar method had been proposed by Boden et al. 3

and Denisyuk et al.4
On the other hand, digital speckle pattern interfer ometry (DSPI) has developed as a powerful tool to perform several operations usually associated with holographic interferometry in the image plane; thus this method is also called digital holography.Defor mation measurements and generation of contours of three-dimensional objects are some examples.5*6 A review of some of these applications can be found in Ref. 7, but a profusion of recent developments exists in the literature.
In its basic form the image of an object with a superposed coherent background is registered by a TV camera and then digitized and stored in a frame memory.Subsequent images are subtracted from the initial image, and the square or the modulus of the difference is shown on a monitor.A phase change between the reference and the object waves is introduced between the first and the final observed states.It can be produced, for example, by a deforma tion of the object or by a change in the illumination conditions.If this phase difference on the image is slowly varying on areas comprising several pixels, then the same speckle pattern is present in both images in regions in which the phase difference is 2-ir or congruent values.In these regions, subtraction produces a dark area in the result.Other phase delays modify the resulting speckle pattern, and the subtraction gives a nonzero response.Fringes are thus obtained in the subtracted image showing the locus of constant phase difference.High resolution inherent to analog holography is not required here.Only the speckle grains must be barely resolved by the imaging system.Three dimensional image for mation is sacrificed, but operation at TV frame rates without chemical developing is obtained as a trade.
We describe now how a DSPI experiment can be modified to obtain a light-in-flight display.For all image places in which the OPD is greater than the coherence length of the light the phase shift is of no consequence.At these points the superposi tion is incoherent; therefore a phase shift in the reference beam does not change the measured inten sify, and subtraction produces a dark output at these points.
In regions in which the superposition is coherent, interference fringes are produced.These fringes are substituted by the complementary ones when the phase shift is introduced and the observed speckle pattern changes.Though the actual fringes are not resolved by the TV camera, subtraction in these The /*-number of the camera lens was set at a relatively high value ( f = 11) so that speckle grains could be resolved by the CCD array.This geometry introduces a certain amount of vignetting, but with a long enough focal length (in our case, 135 mm) in the imaging lens, the best part of the CCD detector area (roughly 1 cm x 1 cm) can be illuminated.
As the experiment is performed in the image plane, it is not necessary to use an object-to-reference-beam intensity ratio greater than 1.This ratio was used in our experiment.
The geometrical aspects of this experiment can be easily understood in terms of the holodiagram.8The two foci of the ellipsoids are in this case the focal point of E, the origin of the beam illuminating the object, and the center of the image forming lens (Fig. 1).
Figure 2 shows the experimental result obtained for the intersection of a spherical wave front with a plane object.The holodiagram constants for this  We have proposed and demonstrated a DSPI experi ment to depict the locus of the intersection of an object with an evolving wave front.Although it is intrinsically a sequential method, it can be imple mented at a TV frame rate without chemical process ing of a holographic plate.The position of the wave front can be changed by the adjustment of a delay line.
This work was supported by Consejo Nacional de Investigaciones Científicas y Técnicas grant PID 3 071700/88 and a grant from Fundación Antorchas.We thank the Laser Group of the Centro de Investiga ciones Opticas for providing the dye laser.J. Po marico is a Fellow of the Comisión de Investigaciones Científicas de la Provincia de Buenos Aires.
Figure 1 shows the experimental setup.A cw argon-ion-laserpumped Rhodamine 110 dye laser is employed (A 550 nm).A piezoelectrically driven mirror (PEM) is used to introduce a Tr phase shift in the reference beam between the two exposures.Lens L conju gates the focal point of the beam expander, E, in the front focal plane of the imaging system of the CCD camera, thus producing a plane wave on the detector array.The image registered by the detector is the superposition of a speckle pattern and a uniform background produced by the reference beam.

Fig. 2 .
Fig. 2 .Intersection of a spherical wave front with a plane-tilted object.

Fig. 3 .
Fig. 3. Intersection of a spherical wave front with the same object after passing through a small parallel glass plate for two different positions of the delay line.