Apparatus and Method for Quantitative Measurement of Small Differences in Optical Absorptivity Between Two Samples Using Differential Interferometry and the Thermooptic Effect

The present invention relates generally to the use of a differential interferometer to measure small differences in optical absorptivity between two weakly absorbing samples located therein, and more particularly to the use of the chanqe in refractive index of a weakly absorbing sample due to the heat generated when an intense laser beam traverses it relative to a second irradiated sample of slightly different optical absorptivity, each of which is positioned in one arm of an interferometer cavity, which change produces a fringe pattern shift which can be related to the difference in optical absorptivity of the samples.

In many instances the detection of trace amounts of dissolved material is complicated by large background absorptions of the solvent. Under such conditions the part of the absorption signal due to the solute can be much smaller than the precision of the measurement of the combined solvent and solute absorption in which case no useful concentration information can be obtained using conventional measurement technology. The apparatus and method of the instant invention allows the solvent absorptivity to be nulled out of the measurements, the resulting absorption related signal being related solely to the solute absorptivity. A cell containing a weakly absorbing solution is placed in each arm of an interferometer. Heat is generated when a laser beam traverses the cells since a certain fraction of its energy is absorbed by the sample causing an increase in temperature. This results in a change in the index of refraction of the solution which is temperature dependent with a consequent change in the optical pathlength of the laser beam through the cell. Such changes in pathlength can be measured with an interferometer. For low-loss media (losses of 10.sub.-4 cm.sup.-1 or less), this effect is very small, and sensitive interferometers in well-controlled environments must be employed. For solutions having the same absorptivity, and for heating beams of equal intensity, the change in optical pathlength produced by laser heating is the same in each cell, and there is no shift in the fringe pattern formed by the interferometer. However, any difference between the absorptivities of the two solutions results in unequal heating and a fringe pattern shift. The degree of fringe movement is a measure of the difference in absorptivity between the two cells. A critical feature of the instant invention, which allows clear resolution of differences in sample absorptivity of approximately 10.sup.-5 cm.sup.-1, is that two fringe patterns are formed using laser beams from the interferometer. A signal fringe pattern is formed by a pair of low-power helium-neon laser beams each of which traverses a sample cell colinearly with a heating laser beam. A reference fringe pattern is formed from another pair of low-power helium-neon laser beams passing through the sample cells narrowly displaced from the heating beams. The purpose of this latter fringe pattern is to stabilize the signal fringe pattern with respect to normal thermal drift. This stabilization is achieved using a movable compensator plate inside the interferometer controlled via a feedback loop which has as its input the fringe pattern intensity at a fixed point which is a measure of the fringe position. It is this stabilization which allows the achievement of the minimum detection limits to be reported hereinbelow, and which represents a significant improvement over that which can be achieved by other methods where the solvent absorptivity is in the range of about 10.sup.-3 cm.sup.-1 or higher using the instant invention. Signals due to solvent absorptivity have been nulled to approximately one part in four hundred which thereby allows the clear resolution of absorptivity differences of about 10.sup.-5 cm.sup.-1 using about 50 mW of laser power. For comparison in the nondifferential configuration of the instant interferometer; that is, a sample cell in only one arm, and with a background absorption of 10.sup.-3 cm.sup.-1, the minimum detectable change in solute absorption is approximately 10.sup.-4 cm.sup.-1 in the best cases. The decrease in minimum detection limit which occurs with differential detection is due principally to the increased precision of the data relative to that obtained using nondifferential techniques.

Although interferometers (refractometers) have been used for over one hundred years to compare the refractive indices of gases, the use of an interferometer to detect weak absorptions using the thermooptic effect was only recently demonstrated.

1. In "Measurements of the Absorption of Light in Low-Loss Liquids," by J. Stone, J. Opt. Soc. Amer. 62, 327 (1972), the author describes a dual-beam interferometer where an intense laser light beam simultaneously heats the single solution under investigation and monitors its change in optical pathlength due to heating and thermal drift, while another laser beam of weak intensity monitors any changes in optical pathlength due to thermal drift alone. Both beams in Stone's apparatus are separated by only a few millimeters and traverse the same solution so that the change in optical pathlengths from drift recorded by the beams are equal. In this way the fringe pattern was stabilized with respect to drift and small shifts in this pattern due to heating could readily be measured. The apparatus could not, however, be used for differential measurements since the fringe pattern is not stabilized if both beams are used to record the thermooptic signal from different solutions. This is the critical feature of the instant invention, not taught by Stone. Our invention teaches the use of a drift stabilizing reference laser beam in each of two sample cells for which the difference in absorptivities is being determined, the stabilization of the fringe pattern resulting therefrom leading to significantly enhanced measurement sensitivity. The instant invention, then, teaches the measurement of changes in refractive index of the two sample solutions due to heating using weak intensity probe laser beams colinear with heating laser beams. Thermal drift in the probe fringe pattern is reduced by the use of a reference set of fringes formed from low-intensity reference laser beams which pass through the sample solutions slightly displaced from the probe and heating beams. A driven compensator plate inside our interferometer is connected to a feedback loop which responds to error signals resulting from thermal drift, which signal is used to keep the reference fringe pattern stable. The drift in the probe fringes was found to be identical to that of the reference fringes due to the proximity of the two sets of beams so that both sets of fringes could be stabilized in this manner, without which the reported sensitivity could not have been achieved.

2. In "Optical Nulling for Trace Analysis Based on The Thermooptic Effect and an Interferometer," by David A. Cremers and Richard A. Keller, Advance Program of the Conference on Lasers and Electrooptics, Washington, D.C., June 10-12, 1981, distributed sometime in April, 1981, and in "Quantitative Measurement of Solute Absorption at Levels Below Solvent Absorption by Optical Nulling Techniques," by D. A. Cremers and R. A. Keller, Los Alamos Conference on Optics '81, Santa Fe, NM, Apr. 6-9, 1981, the authors, who are also inventors of the instant invention, briefly describe the invention in abstract form. However, although both references mention the differential nulling procedure, neither even hints at the fringe stabilization critical in attaining the minimum detection limit quoted hereinabove.

An object of the instant invention is to measure small differences in optical absorptivity between two weakly absorbing samples.

Another object of our invention is to determine the concentration of a solute in solution where the solute absorptivity is much smaller than that of the solution.

Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.

To achieve the foregoing and other objects, and in accordance with the purposes of the present invention, as embodied and broadly described herein, the apparatus of this invention may comprise an interferometer cavity into which is placed two cells containing the samples under investigation, narrowly-spaced probe and reference laser beams which are each split into two widely-spaced, parallel beams after entry into the cavity, one probe beam and one reference beam becoming narrowly-spaced and parallel before entering one of the sample cells, and the other probe and reference beams becoming similarly narrowly-spaced and parallel before entering the second of the cells, the two probe and two reference laser beams being recombined to form a probe and reference fringe pattern, respectively, two amplitude modulated heating laser beams, means for equalizing their intensity and rendering them colinear with the split probe laser beams, one with each, and means for separating them from the probe beams after they exit the sample cells, means for equalizing the intensity and adjusting the parallelism of the two beams in each of the probe and reference beam pairs, means for stabilization of the reference and probe fringe patterns, and means for detecting and recording the probe fringe pattern intensity. Preferrably, the interferometer cavity is of the Jamin design in order to reduce sensitivity of the apparatus to vibrations. It is also preferred that the probe and reference laser beams incident upon the interferometer cavity derive from a single laser source the output of which is divided into two approximately equal intensity parts. Similarly, it is preferred that the heating laser beams derive from a single laser source, the output of which is divided into two approximately equal intensity parts. It is further preferred that each pair of narrowly-spaced probe and reference laser beams be located approximately 5 mm apart. It is finally preferred that the means for stabilizing the reference fringe pattern include a movable compensator plate which is part of a closed feedback loop which further includes means for dithering and driving the plate to provide modulation and adjustment of the fringe pattern necessary for phase-sensitive detection. The compensator plate intersects the probe and reference beams in one arm of the interferometer so that the shift in probe fringes due to a thermooptic-induced response of the interferometer is also modulated at the same frequency as the reference fringes and can be monitored by phase-sensitive detection.

In a further aspect of the present invention, in accordance with its objects and purposes, the method hereof may also comprise splitting incident parallel probe and reference laser beams into a pair of probe and reference laser beams, each widely spaced split probe beam of approximately equal intensity traveling in a parallel direction, and similarly for the split reference beams, one probe and one reference beam emerging narrowly-spaced, and similarly for the second probe and reference beam, inserting a light-transmitting sample holding cell in the path of each pair of laser beams, recombining the two probe beams and the two reference beams to form probe and reference fringe patterns, respectively, introducing the samples under investigation into the cells, superimposing an amplitude modulated heating laser beam to be colinear with each probe laser beam before it enters the sample cell for a specified period of time, each of these heating beams having substantially the same intensity, separating the laser heating beam from each probe beam after each pair has passed through one of the sample cells, stabilizing the reference fringe pattern with respect to drift due to air currents, variations in room temperature, and thermal gradients in the sample cells thereby simultaneously stabilizing the probe fringe pattern, monitoring the probe fringe pattern for movement during the time that the heating laser beams pass through the sample cells, differences in absorptivity of the contents of the cells causing different degrees of heating in each cell as a result of the thermooptic affect thereby changing the refractive index of that cell's contents and consequently its optical pathlength for the probe beam traversing it which in return varies the fringe pattern position, establishing the relationship between the difference in absorptivity of the two samples and the position of the probe fringe pattern with samples of known absorptivity, and relating the position measured for the samples under investigation to a value of this difference in absorptivity. It is preferred that two pairs of narrowly-spaced probe and reference laser beams be separated by about 5 mm in order that the stabilization of the reference fringe pattern will simultaneously stabilize the probe fringe pattern. It is also preferred that the specified period of heating be approximately 10s followed by an approximately 1 min. period of cooling before another heating period and measurement of the consequent probe fringe pattern intensity change is commenced. Preferrably, the probe and reference laser beam splitting and recombining steps are performed using a Jamin-type interferometer in order to make the sensitivity of the absorptivity difference measurements to vibrations minimal. It is finally preferred that the stabilizing of the reference fringe pattern position be accomplished using a fringe position detector, feedback electronics, and a driven compensator plate which intercepts one pair of probe and reference beams.

In summary, then, an apparatus and method for the measurement of small differences in optical absorptivity of weakly absorbing samples using differential interferometry and the thermooptic effect has been developed. The critical feature of our invention is the stabilization against drift of the optical pathlength of the probe laser beams which interrogate the samples under investigation, which differential change in pathlength is related to the absorptivity difference between the samples. It is thereby possible to null out the bulk of the sample absorptivity and measure only this difference with substantial precision. Solute absorptivities of 10.sup.-5 cm.sup.-1 have been measured in solutions with total absorptivity in excess of 10.sup.-3 cm.sup.-1 which is not possible with nondifferential methods. Further, the smallest absorption measured with our invention was about 5.times.10.sup.-6 cm.sup.-1, which is comparable to or below measurements made using other thermooptic techniques. The principal advantages of the instant invention include low detection limits, only one critical alignment--that of the super-position of the probe and heating laser beams, simple analysis of the data, insensitivity to small variations in laser beam profile since the technique does not depend on the formation of a thermal lens, and easily obtained differential thermooptic spectra of solutions. This last use of our invention involves the use of separate probe and heating beams to record the thermooptic signal which permits scanning of the heating wavelength without the problem of phase shifts introduced by dispersion in optical elements through which the beams pass. Since the wavelength of the probe beam is fixed, a phase shift occurs only due to heating of the solutions.

The accompanying drawings, which are incorporated in and form a part of the specification, illustrate an embodiment of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings:

FIG. 1 is a schematic diagram of the apparatus used for differential measurements of weak sample optical absorptions wherein the samples under investigation are located in an interferometer cavity and the thermooptic effect produces a shift in the output fringe pattern of the interrogating probe beams which can be related to the difference in the two sample absorptivities when heating laser beams of equal intensity traverse the samples colinear with the probe beams.

FIG. 2 shows the effect of stabilizing the reference fringe pattern with respect to drift in the probe fringe pattern, curve (a) showing the drift of the probe fringes relative to a baseline with the stabilization circuitry off, while curve (b) shows the drift relative to a baseline with stabilization circuitry activated.

FIG. 3 shows the change in phase-sensitive detector signals, which is related to the change in the probe fringe pattern position, versus the change in solute absorptivity (.alpha..sub.s) for three solvents: water (.DELTA.); CH.sub.3 OH (.quadrature.); and CCl.sub.4 (O).

FIG. 4 shows the comparison of phase-sensitive detector signals, which are related to the shift in the probe fringe pattern, with the instant apparatus in a non-differential (curves (a) and (c)), and differential (curve (b)) configuration.

FIG. 5 compares absorptivity measurements with the apparatus in a differential (O) and non-differential (.quadrature.) configuration with respect to measurement precision as reflected in the precision bars and different ordinate scales.

FIG. 6 is a demonstration that the smallest absorptivity measurable with an embodiment of the instant invention is approximately 5.times.10.sup.-6 cm.sup.-1 for solutions of iodine in carbon tetrachloride the latter solvent an absorptivity of approximately 1.2.times.10.sup.-5 cm.sup.-1.

FIG. 1 is a schematic representation of the apparatus used for the differential measurements reported for the instant invention. The heart of this apparatus is a commercial interferometer of a Jamin design which consists principally of two optically flat glass blocks 19, 20. Two laser beams 3, 4, are incident on the first glass block 19, each being split into two beams. Most usually, the two incident beams hereinafter labelled probe beam 3 and reference beam 4, will be split off as approximately equal intensity beams from a single laser source. The incident and exit surfaces of the glass blocks are reflection coated such that the two beams in the interferometer formed from each of the incident laser beams have about the same intensity when they emerge from the splitting block. After passing through various optical components in the interferometer, the beams are recombined in the second glass block 20 to form two interference fringe patterns. Any differential change between the optical pathlengths of the two beams in the interferometer results in a fringe shift. The Jamin design was chosen because of its reduced sensitivity to vibrations compared to other types of interferometers. The probe beam and the reference beam are low-power helium-neon laser beams (approximately 1 mW), separated by approximately 5 mm. The split probe beam, designated by the solid line, emerges from the first interferometer block as two parallel laser beams of approximately equal intensity, which form two arms of the interferometer. Intensities of the two probe beams are adjusted to be substantially equal using neutral density filters 5, 26 to give maximum fringe visibility on recombination. Similarly, the reference laser beams are split into parallel beams of approximately equal intensity which are represented by the dashed lines in FIG. 1, one of the split reference beams lying parallel and narrowly-spaced from one of the probe beams, while the other reference beam emerges parallel and narrowly-spaced to the second of the probe beams. The two arms of the interferometer, which will be designated as the upper arm and the lower arm, are widely separated. The two emerging reference beams are made to be of substantia11y equal intensity using neutral density filters 5, 26, again for the purpose of giving maximum fringe visibility upon recombination of these beams. Two laser heating beams 1, 2 are made colinear with the split probe beams, one with each, using dielectric coated mirrors 6, 7 (2.5 cm dia..times.0.95 cm thick, 99% reflectivity at 515 nm, 66% transmission at 633 nm). In the instant invention, the two heating beams are derived from a single argon-ion laser operating at 515 nm the output of which was split into two approximately equal beams. The intensities of the two heating beams were made substantially equal before entering sample cells 11, 12 by rotating thin glass plates 9, 10 to control the amount of light reflected out of each beam. A pair of wedged quartz plates (30' wedge) 25 were positioned in the upper arm to correct for any deviation of the beams from nonparallel paths through the interferometer introduced by other wedged optical elements (e.g., cell windows). These wedged plates were necessary to insure that the helium-neon laser beams recombined in the second glass block are colinear when they are merged. Two 5 cm long spectrometer sample cells 11, 12 are inserted into the two arms of the interferometer, one into each arm, in such a way that one set of three laser beams traverses each (the probe beams colinear with the heating beams and the two reference beams approximately 5 mm away from the heating beams). A diffraction grating 8 located after the sample cells separates the heating and probe beams. In this way, the heating beams do not pass through the glass blocks forming the interferometer, eliminating problems associated with heating of the glass blocks which may lead to an unwanted thermally-induced probe fringe shift. The helium-neon probe and reference laser beams in the lower arm of the interferometer then pass through a galvanometer-driven compensator plate 15 that was part of a closed feedback loop used to stabilize the reference fringe pattern with respect to drift due to air currents, variations in room temperature and thermal gradients in the samples. This compensator was dithered to provide modulation of the fringe pattern position necessary for phase-sensitive detection. Other components of the feedback loop were the galvanometer control electronics, a lock-in amplifier, and a photodiode. Fringe stabilization was necessary because the measurements reported here involve the detection of fringe shifts due to changes in optical pathlengths as small as about 1/200 of the helium-neon wavelength. Stabilization was achieved using the principle also used by the author of reference 1 who noted that drifts in the probe and reference fringes are equal if the beams in the interferometer travel over approximately the same paths. This has been found to be the case in our interferometer for probe and reference beams in each arm separated by approximately 5 mm. Therefore, stabilization of the reference fringes with the galvanometer-driven compensator also stabilize the probe fringes. The probe laser beam in the upper arm passes through a manually operated compensator plate 16 which permits independent adjustment of the optical pathlength of this beam through the interferometer. The four helium-neon beams then enter the second glass block 20 of the interferometer and are combined into two fringe patterns. Each set of fringes was expanded by a negative lens 21 to approximately 4 cm diameter and observed on one of two screens 17, 18. Typically, two or three complete fringes could be seen on the screen. The positions of the fringe patterns can be determined by monitoring these intensities at points on the screens through small holes (1.1 mm dia.) using photodetectors 22, 23. The entire apparatus was shielded from room air currents by a clear-plastic cover.

The shift in probe fringes due to the thermooptic-induced response of the interferometer which is related to the difference in optical absorptivity of the two samples was monitored using a photomultiplier tube 23 and a second lock-in amplifier tuned to the dither frequency of the compensator plate 15. Entrance and exit ports 13, 14 on the sample cells permit measurements on flowing samples. Heating of the solutions was initiated by opening a shutter 27 that blocked the argon-ion laser beam. Prior to measurement of the fringe shift, a check was made to insure that a minima of the fringe pattern was centered over the hole in the screen (approximately 0 V lock-in amplifier signal). Generally, resetting of the probe fringe pattern using the manual compensator 16 to put a probe fringe minimum over the hole in the screen was not necessary because relative drift of the reference and probe fringes was long-term (approximately 1 hour). Immediately before opening the shutter, the lock-in amplifier voltage was recorded to give an initial value for this quantity. The shutter was then opened for approximately 10 s and a second lock-in amplifier voltage was recorded. The difference in these two voltages was the lock-in amplifier signal due to heating of the solutions. The solutions were allowed to cool for at least one minute before another measurement was taken.

FIG. 2 shows the drift of the probe fringe pattern with the stabilization circuitry on and off. The curves represent the lock-in amplifier signal over a period of approximately 80 s. The straight horizontal lines are the baselines; about 0 V. Curve (a) describes the drift of the probe fringe pattern with the stabilization circuitry off. This drift is approximately -4 V. Curve (b) is the drift of the fringes with the stabilization circuitry on. It is apparent that with the fringes stabilized, the amount of drift is reduced by a factor greater than 100.

The response of the apparatus to a change in the optical pathlength of one probe beam through the interferometer was investigated using a second galvanometer-driven compensator plate. That is, the relationship between the probe fringe intensity as viewed through the hole in the screen, hereinafter referred to as signal intensity, and the change in optical pathlength of the probe beams through the interferometer was determined by varying the rotation angle of the compensator plate which changes the optical pathlength in a predictable manner. A linear relationship was found between the change in optical pathlength and the signal intensity, which indicates that this signal intensity, which is related to the lock-in amplifier output voltage, is directly proportional to the difference in optical absorptivity between the samples, .DELTA..alpha.. This later relationship can be proven theoretically and holds for values of optical pathlength changes of up to at least 3.times.10.sup.-6 cm. For very large changes in optical pathlength, this linear relationship breaks down. However, this is not a serious limitation because the response of the apparatus to a change in optical pathlength can be easily calibrated.

FIG. 3 shows the lock-in amplifier signal versus the change of solute absorptivity, .alpha..sub.s, for three solvents; water (.DELTA.); methanol (.quadrature.); and carbon tetrachloride (O). Small additional amounts of solute were added to the solution in one sample cell in the interferometer to produce a differential response. The methanol data were obtained with a background absorption of 2.3.times.10.sup.-3 cm.sup.-1 in each cell. The data for water and carbon tetrachloride were obtained using the background absorption of the pure solvent. For water this was about 3.times.10.sup.-4 cm.sup.-1, and for carbon tetrachloride about 1.2.times.10.sup.-5 cm.sup.-1. The heating laser power was about 50 mW for both carbon tetrachloride and methanol, and about 100 mW for water. The solutes employed were cobalt sulfate for water and methanol, and iodine for carbon tetrachloride, and the lock-in amplifier readings were taken 10 s after the argon-ion laser beam was unblocked. The predicted linear relationship between the difference in optical absorptivity between the two samples and the lock-in amplifier signal is confirmed for the three solutions employed.

FIG. 4 shows the comparison of lock-in amplifier signals with the instant apparatus in a non-differential mode of operation (curves (a) and (c)), and a differential mode of operation (curve (b)), and shows the ability of this apparatus to null out absorptions of equal strength. In curve (a), one cell contains pure methanol, with an absorptivity of approximately 1.5.times.10.sup.-4 cm.sup.-1, and the other cell contains a cobalt sulfate/methanol solution having an absorptivity at (515 nm of about 2.3.times.10.sup.-3 cm.sup.-1). In curve (b), both cells contain the cobalt sulfate/methanol solution having an absorptivity at 515 nm of about 2.3.times.10.sup.-3 cm.sup.-1, and shows the ability of the instant apparatus to null out absorptions of equal strength in the differential interferometer mode of operation. In curve (c), the solutions in curve (a) are interchanged between the two cells. The initial spike on each curve indicates the start of the heating of the solutions when the argon-ion laser beam is unblocked. The heating period lasts for approximately 10 s. Typically, signals due to the background absorptions could be nulled out to better than one part in 400. The null signals in these cases were on the order of the normal drift of the interferometer over a period of about 10 s; that is, approximately 0.02 volts.

FIG. 5 shows a comparison of differential (O) and non-differential (.quadrature.) measurements of solute absorptions ranging between (0.23-4.6).times.10.sup.-4 cm.sup.-1 in the presence of a background absorption of 2.3.times.10.sup.-3 cm.sup.-1. For the differential measurements, the background absorption of each solution was adjusted to be initially 2.3.times.10.sup.-3 cm.sup.-1. Small amounts of a concentrated solution of CoSO.sub.4 /CH.sub.3 OH were then added to one cell to generate a differential signal. For the non-differential measurements, one cell contained pure methanol and small amounts of the concentrated solution were added to the other cell which had a minimum background absorption of 2.3.times.10.sup.-3 cm.sup.-1. In both cases, the background absorption was provided by cobalt sulfate dissolved in methanol. The reduction in noise of the differential data, which is evidenced by the very much smaller precision bars on the data points, clearly demonstrates the superiority of nulling out background absorptions in order to measure solute absorptions that are significantly smaller.

FIG. 6 shows the investigation of the detection limit of the interferometer for carbon tetrachloride. Solute absorptions of .about.5.times.10.sup.-6 cm.sup.-1 could be detected (with signal-to-noise ratio of approximately 2) using laser powers of approximately 100 mW. The absorptivity of CCl.sub.4 at 515 nm is listed in the literature as 1.2.times.10.sup.-5 cm.sup.-1 which was the background absorption in each cell. Using methanol and a laser power of about 50 mW, increases in absorptivity of one cell of approximately 2.times.10.sup.-5 cm.sup.-1 could be detected in the presence of a background absorption of 2.3.times.10.sup.-3 cm.sup.-1. The poorest detection limit was found for water. For a laser power of approximately 100 mW, the smallest solute absorptivity measurable was about 3.times.10.sup.-4 cm.sup.-1 for this solvent. The difference in detection limits is a result of the different thermooptic sensitivities of the various solvents; for example, the change in refractive index of water with temperature is very much smaller than, say, carbon tetrachloride.

The solution cells, wedged plates, and dielectric-coated dichroic mirrors inside of the interferometer were made of fused quartz which has a smaller optical absorption than pyrex or glass. Reference 1 indicates that it is especially important that the solution cells be made of fused quartz (or other weakly absorbing transparent material) because pyrex cell windows absorb some of the heating laser beam energy which is passed on to the liquid, resulting in a transient signal resembling actual absorption of the laser light by the solution. Even quartz cells may produce noticeable heating of the solutions at increased laser powers or when small absorptivities are measured (<10.sup.-5 cm.sup.-1). To a first approximation, however, in the differential measurements of the instant invention these effects are to a good degree nulled out. Dilute solutions were generally prepared from more concentrated solutions by simple volumetric dilution. These dilute solutions were then pipetted into the sample cells which remained in a fixed position inside the interferometer. It was necessary to wait about 10 to 15 minutes before making measurements to allow turbulence and thermal gradients within the samples to subside. A total of 12 measurements were taken with each solution. The total length of the precision bars shown in the figures here and above is twice the standard deviation.

The null response of the apparatus of the instant invention was found to exceed the limits attributable to normal drift of the signal under two separate conditions: (1) use of heating laser powers greater than about 100 mW, regardless of the solution absorptivity, and (2) when the power absorbed by the solution exceeds approximately 1.5.times.10.sup.-4 W/cm. The first condition was caused by heating of the optical components in the interferometer and may be avoidable with a different arrangement of the components (e.g., moving the wedges to a position after the grating so that they do not intercept the heating beams). It was not possible to single out any particular component (s) as being the main source of the signal at increased laser powers. The second condition is the result of convection and/or thermal lensing. Thermal lensing, which reduces the on-axis intensity of the probe beam, may be a source of spurious signals in our detection system because a change in probe intensity at the photodetector results in a lock-in amplifier signal resembling a fringe shift. Thermal lensing was not important in the experiments reported hereinabove, however, because the laser beams were not focused into the solution cells as in thermal lensing experiments. At increased laser powers and/or absorptivities, though, thermal lensing could become noticeable without focusing.

It should be mentioned at this point that the measured signal intensity derived from the instant interferometer is strongly dependent upon the quantum yield for conversion of absorbed laser radiation into heat in the solution. Generally, this quantum yield is near unity in which case the measured absorptivity and measured absorptivity differences reflect the true absorptivity. In the situation where this does not obtain; that is, the quantum yield is substantially less than unity, appropriate corrections must be made when quoting measured absorptivities.

Also to be noted is that since different materials exhibit different temporal thermal responses, it is imperative that the major constituent of the samples in each arm of the interferometer be identical.

It has been demonstrated that the interferometer is an effective method of nulling large background absorptions due to solvent or solute. In the differential mode of the interferometer, the signal that would be produced by the interferometer in the non-differential configuration was supressed by a factor of about 400. With the background signals suppressed, differences in absorptivities between the cells .about.1/100th of background were measured. In addition, the smallest absorption measured with the interferometer was approximately 5.times.10.sup.-6 cm.sup.-1, which is comparable to that actually measured using other thermooptic techniques. The principal advantages of differential interferometry are:

(1) the method has a detection limit comparable to that demonstrated for other thermooptic-based techniques;

(2) the physical principles which produce the signal are easily analyzed and do not increase in complexity in going from a non-differential to a differential configuration of the apparatus;

(3) the only critical alignment of the apparatus is the superimposing of the axes of propagation of the heating and probe laser beams;

(4) the long term stability of the apparatus of the instant invention is very good (.about.1 week). The technique is insensitive to small variations in laser beam profile; and

(5) the apparatus of the instant invention is especially useful for recording differential thermooptic spectra of solutions. The use of probe beams separate from heating beams to record the thermooptic signal permits scanning of the heating laser wavelength without the problem of phase-shifts and beam diffraction introduced by dispersion in optical elements through which the beams pass. Since the wavelength of the probe beam is fixed, a phase-shift occurs only due to the heating of the solutions.

The foregoing description of a preferred embodiment of the invention have been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiment was chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.