Anal. Chem. 7987, 59, 1446-1452
7446
Resolution and Dynamic Range Considerations in Hadamard Transform Photothermal Deflection Imaging Fotios K. Fotiou and Michael D. Morris* Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109
Photothermal deflectlon measurements over compounds depodted on thkr-layer chromatography plates were performed by uslng a spatlally encoded expanded Ar’ laser beam. A serles of Hadamard masks were used to encode the laser beam. Masks wlth 63-255 actlve elements and 300-25 pm element w#dthswere used to study the dynamlc range of the system and the resolutlon capablitty of the Imager. The effects of magk aperture wldth, mask moth, mask construction technology, and anakgtodlgltal converter dynamic range are Investlgated.
The potential for application of photothermal deflection spectroscopy (PDS) for ultrasensitive analysis has been extensively studied (1-4). Sensitivity comparable to fluorescence detection has been demonstrated, making the technique a potent alternative for the detection of nonfluorescent compounds. The method has also been successfully applied for nondestructive evaluation and thermal characterization of materials (5-7). According to theory (8,9) the photothermal signal intensity is proportional to the energy deposited on the sample. However, high-power irradiation from continuous wave (CW) lasers and even moderate- or low-energy irradiation with pulsed lasers jeopardize the integrity of the sample. Distribution of the laser energy over the total sample surface is necessary in order to minimize or avoid the thermal damage and retain the inherent sensitivity of PDS. Coufal and coworkers have demonstrated the feasibility of power distribution in photoacoustic spectroscopy by using both Hadamard (10) and Fourier (11)coding of the expanded excitation beam. Hadamard masks are simpler to construct, while Fourier (sinusoidal) masks allow variable resolution from a single mask. Fournier and co-workers have applied tomographic reconstruction of PDS signals from a line focused laser for investigation of subsurface defects (12). We have demonstrated the feasibility of the power distribution for photothermal measurements by Hadamard coding of a pulsed excimer laser (13) and a CW laser (14). In the latter case we have shown that there is only a slight sensitivity loss relative to measurements made with a focused beam. All previous work in the field of photoacoustic and photothermal Hadamard coding (10,13,14) has been performed with masks containing only a small number of coarse elements. Coufal employed masks with only 7 or 15 active elements with a width of 0.4 mm. Our own studies employed a mask with 35 active elements with element width of 0.4 mm. However, Hadamard encoding would be of greater use for higher spatial resolution imaging. For such applications masks with finer elements and many more elements are required. In this paper we evaluate Hadamard transform encoding for photothermal measurements at moderate resolution and with realistically large numbers of elements. We assess also the resolution requirements for the data acquisition system.
THEORY In Hadamard transform photothermal spectroscopy, the pump laser beam is expanded to illuminate many resolution 0003-2700/87/0359-1446$01.50/0
elements along a line or over an area simultaneously. The probe beam propagates along this line and parallel to the sample surface sequentially interrogating all the refractive index gradients generated by the pump beam. Therefore, because photothermal signals are additive (12-14), the observed signal will be the sum of the signals from each of the illuminated elements x . If the pump beam is spatially encoded with n suitably chosen masks ( 1 5 ) , the signals from the n resolution elements can be recovered from the set of n independent linear equations for n different mask configurations. In matrix notation, the set of equations may be written as eq 1.
Y =
sax
(1)
In equation 1, Y is a matrix consisting of the measured photothermal signals yi for the n mask configurations. X is a matrix representing the individual photothermal signals xi for the n positions on the plate. The matrix S describes the configurations of the n masks and is an S-matrix. S-matrices are derived from Hadamard matrices (15).The decoded data can be recovered by eq 2.
x = s-1.y
(2)
Image degradation in a multiplexed measurement can result from the limited dyamic range of the transducer or the analog to digital converter (ADC). In imaging theory the phenomenon is called the contouring effect (16). If a mask system of n = 2j resolution elements is used and if the dynamic range of “brightness levels” for every resolution element is 2K:1,then a total of j + k bits describes the image under study. However, since the digitized signals are sums of the individual signals, only n signals must be digitized. Therefore, a smaller dynamic range is required than the total number of bits needed to represent the total sample surface. The number of bits needed depends on the difference between the values of the largest and smallest signals to be digitized. Assuming that the least significant bit is used for the representation of noise, the number of bits b, required to digitize the image of a surface composed of regions of different intensities is given approximately by eq 3.
b=j+k-4
(3)
For example, if the range of sample intensities is 24,a 255 element mask requires only an 8-bit ADC. Any ADC can have its dynamic range apportioned between a number of mask elements and signal dynamic range, as required. A 12-bit converter could easily handle a mask with 4095 elements, under most actual sample conditions. Equation 3 describes only the dynamic range of the converter required to digitize an image. The low dynamic range results from the roughly Gaussian distribution of Hadamard-encoded intensities usually observed (17). Most of the ADC readings will be clustered about the average value, with a range that depends largely upon the range of intensities in the image. The low dynamic range requirement is one of the factors that has made Hadamard transform processing attractive for digital image transmission. It has been shown that 0 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 10, MAY 15, 1987
the transmiasion of a Hadamard encoded image is leas sensitive to bit errors and has a lower transmission bandwidth requirement than the image itself (17,18).Similar results have been reported for the transmission of Hadamard encoded speech signals (19). The fundamental limit to resolution in any optical system is diffraction. In practice, other effects such as lens aberrations determine the actual resolution limits. Resolution in an optical system can be most conveniently described by the modulation transfer function (MTF),which is the magnitude of the optical transfer function (20, 21). The MTF is useful because the phenomena that contribute to resolution generally contribute independent and multiplicative terms to the MTF. The MTF is strictly defined only for incoherent illumination. A plot of contrast vs. spatial frequency is usually interpreted as the MTF even for systems illuminated with a coherent beam. A Hadamard-encoded photothermal deflection system presents some complications in the definition of MTF. Several effects may contribute to the overall frequency response. These include thermal diffusion in the sample, diffraction by the edges of the apertures, spatial averaging by the large and finite width of the unit aperture, and blur from motion of the mask. The system might behave as independent apertures, or as an ensemble of randomly distributed unit apertures. Although the properties of the probe beam and detector may also contribute to the observed MTF, we assume that these behave nearly ideally. The system is sufficiently complicated that a rigorous theoretical formulation of the modulation transfer function is not practical yet. We can estimate the effects of several important phenomena and identify most of the major contributions to the system MTF. We neglect the contributions of lens aberrations, which typically become important at higher spatial frequencies than we will be concerned with. Similarly, we do not include the MTF of the photographic emulsion used to prepare masks for this study, but work only with masks for which the emulsion effects are small. The contribution of diffraction of the MTF of a rectangular aperture of width d is given by eq 4. (4) In eq 4, A is the triangle function and fo = d/2Xdo, where X is the wavelength of the heating beam and do is the distance of the mask from the sample. In addition, the finite width d, of the aperture adds another convolution term, a triangle function given by eq 5.
If the mask is moved continuously, rather than incrementally, resolution loss from the motion occurs (15). T o a first approximation, the blur contribution to the transfer function can be considered a result from a rectangular aperture of width equivalent to the time over which the motion is averaged. The equivalent width is the mask velocity, v multiplied by the time constant of the signal processing system, 7. Thus, eq 6 de-
M" = N f x v 7 )
(6)
scribes the blur term in the transfer function. Thermal diffusion in the sample adds another term, which we approximate as another rectangular aperture, whose width is the thermal diffusion length a t the laser modulation frequency, p = ( ~ C Y / W where ) ' / ~ , CY is the thermal diffusion length and w is the heating beam modulation frequency. This term defines a triangular contribution to the MTF, eq 7.
Mt = AVXPCL)
(7)
The overall transfer function is approximated as the product of the several contributions, eq 8.
M = Md
X
Ma X M ,
X
M,
1447
(8)
In the far field, the Hadamard mask is a random array of apertures. For far-field illumination, the ensemble MTF, M, is related to the MTF of an individual aperture by eq 9 (22). (9) The fraction of the total mask area containing apertures if p . In the present case, p = 0.5. Equation 9 predicts an averaging behavior that will make the system respond to higher spatial frequencies than a single aperture of unit width. Our experiments use masks with unit apertures of 25-300 wm widths. From eq 4-9 the effects of diffraction should be small compared to the effects of convolution with the aperture width, motional blurring, if present and the thermal diffusion length. With good heating beam collimation the sample will be in the near field, and ensemble effects should be negligible. Therefore, the MTF should be dominated by contributions from aperture width, blurring, and thermal diffusion in the glass or quartz sample. The MTF should be parabolic in spatial frequency. The aperture width and blur contributions are easily calculated from the properties of the mask and the drive system. The thermal diffusion contribution can be estimated from the thermal properties of the substrate. Of the three contributions, only the thermal diffusion term depends on heating beam modulation frequency. If thermal diffusion is an important contributor to the resolution of the system, the effect will be observed by measurements over a range of modulation frequencies.
EXPERIMENTAL SECTION The masks used in these experiments were fabricated photographically. The mask pattern was drawn with a high-resolution plotter, capable of 25.4-pm step size. The plotter was controlled by a program that converted the desired mask sequence into inked and uninked rectangles, with widths proportional to the number of contiguous open or closed elements. The lines drawn were calculated to include the effect of the line width of the plotter pen, about 0.3 mm. To minimize errors due to irregularities in the lines, the patterns were plotted with resolution elements of 0.7-2 mm. The element width was chosen to be as large as possible consistent with a total mask length of about 30 cm. This length was the maximum value for which photographic reduction was possible. The plots were then reduced to the desired dimensions (1.2-4 cm, overall length) by photography onto Kodalith film (Eastman Kodak). The photographic negatives were mounted between glass plates for rigidity and used as the actual masks. The aperture for each mask system was a pair of parallel razor blades, adjusted to the appropriate spacing. The optical system for most of these experiments was similar to that used previously (14). A Lexel Ar+ laser, operated at 488 nm, was used to irradiate the sample surface. The power delivered to the sample ranged from 2.5 mW to 13 mW depending on the size of the mask being used and on the optical arrangement. The generated refractive index gradients were probed by a H e N e laser, which was parallel to the line defined by the focused Ar+ beam and to the sample surface. The excitation beam was usually shaped by two cylindrical lenses as previously described (14). A telescope consisting of two parallel cylindrical lenses (focal length (fl) 40 and 300 mm) was used to expand and roughly collimate the beam along the probe beam direction. For transfer function experiments, the divergence was adjusted to be less than 1mrad. For most experiments with thin layer chromatography plates, the beam was uncollimated. For certain experiments, the beam was roughly collimated, and made convergent with an angle of about 14 mrad. Another 50-mm fl cylindrical lens was positioned 5 cm above the plate and was used to focus the expanded beam perpendicular to the probe beam direction. The pump beam was modulated with a mechanical chopper and the photothermal signal was demodulated with a lock-in amplifier as previously described. For transfer function mea-
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ANALYTICAL CHEMISTRY, VOL. 59, NO. 10, MAY 15, 1987 211 -
Table I. Hadamard Masks Used mask I I1 111 IV V
VI a
14 -
active elements
element width, Wrn
imaging length, mm
intensity, mW
63 127 127 127 255 255
299.0 150.9 99.2 59.7 49.6 25.0
18.9 19.2 12.6 7.6 12.6 6.4
10 12 6.5 4 13" 2 . P , 7'
22
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z 9
10
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f z
z
YI
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Roughly collimated beam. Uncollimated beam.
surements, the modulation frequency was varied from 20 to 730 Hz. For most other experiments the modulation frequency was 7 Hz. The six masks used are described in Table I. The masks contained 2N - 1elements, to yield N active elements as shown in Table I. The table includes the imaging line length, the size of the resolution element, and the total power delivered to the sample surface. The mask translation and data acquisition systems previously described were employed here (14). Data transformation was performed with FORTRAN programs on a PDP-11/03 microcomputer. Modulation transfer functions were measured by using USAF 1951resolution targets fabricated as positive silver images on glass substrates (Melles Griot 04 TRP 001). Sample for other experiments were spots of trans-azobenzene deposited on Merck silica gel 60 HPTLC plates as previously described (14). They were not subjected to chromatographic development.
I
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6
1
8
I
IO
12
DISTANCE (mm)
Figure 1. Top: Photothermal image from the section of USAF 1951 resolution target containing 1.12, 1.26, 1.41. 1.59 line pairslmm. Data collected with mask 111. Bottom: The actual image of the section of the target. I
,
RESULTS AND DISCUSSION The photographic technology used for mask fabrication could not produce perfect masks. The emulsions contained small bubbles, easily visible under a microscope, which contributed to a scattering loss of about 30% of the incident light. In all masks a filamentous region of 20-30 pm was observed at the edges of each nominally opaque segment, while the bulk of the blackened regions had an optical density greater than 4. For masks IV,V, and VI the partially blackened areas were a significant fraction of the unit element width. The uniformity of the resolution elements was estimated by measurements on the original artwork for masks V and VI. The original drawing has a sequence length of approximately 26 cm. The pattern is composed of two identical subsequences, each about 13 cm long. Measurements were made on sequences of 10 apertures beginning at approximately l/lo, 2/ etc. along the first half cycle. The resolution element was found to be 0.694 f 0.093 mm long. Thus the plotting procedure yields adequately uniform elements. We do not have access to measurement equipment adequate to determine how well this uniformity is preserved in the photographic reduction, however. The mask sequences chosen for these experiments generated matrices of 63, 127, and 255 elements, which are values of 2'" - 1. These sequences were chosen to be amenable to inversion by the fast Hadamard transform (15). Most data transformations were actually carried out by a conventional matrix inversion technique, which was simpler to implement. The 255-element matrix required about 44 s of computation time on our PDP 11/03 computer and the 63-element matrix required about 1.4 s. For comparison purposes, we implemented a fast Hadamard transform (FHT)for the 63-element matrix, using the algorithm of Harwit and Sloane (15). The F H T program transformed the raw data in 92 ms, a factor of 15.2 faster than the direct matrix multiplication required. This improvement suggests that tighter coding could improve the execution time of at least the conventional inversion routine substantially. The transfer function of mask I11 was measured with heating beam modulation frequencies of 20-730 Hz. The
0
1
2
3
4
5
SPATILL FREQUENCY (Ip/mm)
Figure 2. Coherent transfer function of Hadamard PDS system at 20 Hz (El), 371 Hz (A),and 730 Hz (+). Data collected with mask 111. Solid line: product of motional blurr and aperture blur transfer function contributions.
99-pm unit aperture is the smallest for which photographic development problems could be assumed to make only minor contributions to the transfer function. Because coherent illumination was used, the measured function is the coherent transfer function rather than the true modulation transfer function (20). For these experiments, continuous mask movement was used, although this introduces a blur into the image. We have previously demonstrated (14) that continuous and stepwise motion give the same results in thin layer chromatography densitometry, where only low resolution is needed. Therefore, blur was accepted as the cost of eliminating the time delays associated with incremental motion of the dc motor system. Figure 1 shows the photothermal images from a section of the resolution target containing 1.12-1.59 line pairs/mm. The heating beam was modulated a t 371 Hz. Similar quality images were obtained at modulation frequencies from 19 to 730 Hz. The usual inverse relation between signal intensity and modulation frequency was observed. Some data could be obtained a t modulation frequencies as high as 1500 Hz. Low signal-to-noise ratios precluded measurements over a wide enough contrast range to provide useful estimates of the transfer function a t frequencies above 730 Hz. Figure 2 shows the coherent transfer function for heating beam modulation frequencies 20, 371, and 730 Hz. Measurements were reproducible to about &lo%. Each point is
ANALYTICAL CHEMISTRY, VOL. 59, NO. 10, MAY 15, 1987 110
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Figure 3. Data collected with uncolllmated beam: (A) data collected with mask I; (B) data collected with mask 11; (C) data collected with mask IV; (D) data collected with mask V I .
the average of three to six measurements. Data taken at 130 and 544 Hz fall into the same region. These data points are omitted for visual clarity. The contrast data show no modulation frequency dependence over the entire 20-730 Hz range. Thermal diffusion lengths vary inversely with the square root of modulation frequency. Our experiments provide almost an order of magnitude change in thermal diffusion length and should reveal a t least a strong dependence. We conclude that the transfer function of the system is not dependent on thermal diffusion, at least with a 99-pm mask element. The transfer function data can be adequately described by the product of aperture and motion blur terms, eq 5 and 6. The solid parabolic curve in Figure 2 is a plot of the product of those equations obtained by using the experimental aperture cutoff spatial frequency of 10 line-pairs/mm and the blur cutoff spatial frequency of 4.8 line-pairs/mm. We conclude that the mask behaves as a system of independent apertures of 99-pm width, whose resolution properties are defined by the aperture width and motion blur, if present. With 127 active elements, the mask is a large random array of slits of constant aperture. In independent experiments we examined the far field diffraction pattern from mask 111. A single slit type pattern was always obtained. The pattern remained completely unchanged as the mask was translated. The same behavior was observed with the other masks. These experiments confirm that the near-field independent aperture approximation is adequate to describe the Hadamard transform system. Thin layer chromatographic plates were chosen to evaluate several aspects of the performance of masks with more elements and finer unit elements. Chromatographic plates and
related materials, e.g. electrophoresis blotting membranes, are the materials for which the present technique is proposed. Because samples on plates are at least 1-2 mm in diameter, thay can not provide tests of the spatial resolution of the system. However, they do provide useful tests of the ability of the transform method to work with masks with realistically large numbers of elements and with systems where both large and small signals are present simultaneously. Figure 3A shows the transformed images from data collected with mask I in place. The sample contained 13 spots of trans-azobenzene deposited in a straight line on approximately 1.1-1.3-mm centers. Each spot contained 150 ng of analyte and was about1 mm in diameter. The width and position of the peaks in the plot agree well with the actual sample. The nonidentical peak areas are primarily a consequence of the Gaussian power distribution in the line-focused heating laser (14)rather than of errors in the positioning and tilt of the probe beam. Empirical corrections for these factors (14) were not applied to these data. Figure 3B shows the images from 7 spots of 150-ng quantities of trans-azobenzene obtained by using mask 11. In Figure 3C, mask N was used to generate the image of 5 spots of 250 ng each. In Figure 3D, mask VI was used to generate an image of 2 spots of 400 ng each. In all cases, the spots were approximately 1mm in diameter at 1.1-1.3 mm intervals. In all cases the heating beam was uncollimated, with a divergence of about 60 mrad. Inspection of Figure 3 shows that the data quality gradually decreases in the progression from mask I, Figure 3A (63 elements, 299 pm), to mask VI, Figure 3D (255 elements, 25 pm). Position and intensity information is recovered from the first three data sets with increasing relative errors. Information
ANALYTICAL CHEMISTRY, VOL. 59, NO. 10, MAY 15, 1987
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Figure 4. Data collected with a roughly collimated beam: (A) Hadamard mask VI was used; (6)mask V was used. about the sample is badly degraded in Figure 3D. The existence of two peaks might be inferred. The spot sizes and the relative areas under the peaks do not agree at all with the actual values. That an uncollimated heating beam is an important cause of image degradation is illustrated by comparison of the data in Figure 3D and Figure 4A. In collection of the data for Figure 3D, the heating laser was left uncollimated. Collection of the data for Figure 4A was carried out with the heating laser collimated to about 14 mrad of divergence. In this case, the correct widths and spacings of the sample spots have been recovered. The relative intensities are approximately as expected for data that has not been corrected for laser power distribution. That overlap of the masked laser radiation is important was readily verified by visual inspection of the beams after passage through the mask. No light and dark regions were visible in the uncollimated beam. The mask pattern was visible only if the beam was collimated before the mask. Similar behavior was observed with mask V. Badly blurred images were obtained with an uncollimated beam. Collimation restored the performance of this mask, as shown in the images of seven 230-ng spots in Figure 4B. All seven peaks have the correct spacing and widths. Their apparent areas can be fitted to a Gaussian distribution, as expected. Thus, approximate collimation is necessary if the mask element width is less than or equal to 99 Mm. The collimation requirements become increasingly stringent as the width of the unit aperture is decreased. In mask VI the limitations of the available photographic technology were apparent. Closed apertures of 1or 2 element widths were not composed of uniformly opaque silver. Instead,
the filamentous structure of the silver was clearly visible through a microscope. Mask VI yields fairly good images only because of the energy redistribution properties of the Hadamard transform. Much of the mask consists of runs of several open or closed apertures. Most of the length of the mask is actually opaque or transparent, as required. Only regions where there is a transition between an open and a closed aperture contribute to image degradation from incomplete blackening of the film. Film imperfections contribute to system degradation in another manner. Under the microscope, small bubbles are visible in the transparent regions of the film emulsion. These bubbles are scattering centers, which reduce the transmittance of the film. Scattering and the Fresnel reflections at the glass and film surfaces reduce the transmission of a nominally transparent region of the mask to about 60%. Figure 5 demonstrates the effect of analog-to-digital converter dynamic range. Although the plate contained 13 nominally identical quantities of azobenzene, the Gaussian intensity distribution in the heating laser provides about a 10-fold range of signal intensities. The plots show the effect of synthetically decreasing the dynamic range of the data used to generate the image of Figure 3A. The original data were obtained with a 12-bit ADC and the system was adjusted to use most of the full range of the converter, 3150 counts out of 4096. The data in the file were truncated to 10,8, 6, and 4 bits, respectively. A random 1 or 0 was then added to the least significant bit. The modified data were then processed through the Hadamard transform to yield the images. From eq 3, a 63-element mask and a 10-fold (3-4 bits) range of signal intensities should require a 5-6-bit converter to represent the image. Indeed, close inspection is needed to see the effects of dynamic range loss in Figure 5A,B. The large number of bits is needed only to describe regions of high curvature. Our data do not contain much high-frequency information, which would be most affected by limiting dynamic range to 8-10 bits. Inspection of the base line noise in the 2-3-mm region and the small peaks in the 15-19-mm region, shows some loss of detail. Further loss of detail leads to noticeable distortion a t 6 bit dynamic range, Figure 5C. This is the limit predicted by eq 3. As Figure 5D shows, 4-bit resolution is clearly insufficient to represent the data. The peaks are almost indistinguishable from noise. Similar effects would be expected in any application of Hadamard photothermal imaging. With a 4-bit range of intensities in an image, a standard 12-bit ADC would be adequate to handle a mask system containing 212 - 1 = 4095 elements. The distribution of data values in the measurements for Figure 3A is surprisingly narrow. Figure 6A is a histogram showing the number of occurrences of each ADC reading in the data file. The total range is only 600 counts. The counts are distribued in a rough Gaussian, centered around 2850 counts. Because of the pseudorandom nature of the mask sequence, many mask positions yield similar total signals. That the Gaussian distribution is not an artifact of the Gaussian laser intensity distribution is shown by the simulation in Figure 5B. In this simulation, the expected distribution of data points is calculated for the 63 element mask and a sample consisting of 13 rectangles 1unit high and 4 units wide with spacings approximating those of the sample in Figure 3A. As in the experimental data, the distribution of data points is approximately Gaussian. Other simulations were performed to calculate the necessary dynamic range for images similar to the plots shown in Figures 3 and 4. We assumed a 12-bit ADC with two bits used to represent the noise. The simulation samples were composed of groups of spots having various intensities within each spot,
ANALYTICAL CHEMISTRY, VOL. 59, NO. 10, MAY 15. 1987 32
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Figure 5. Simulations of data shown in Figure 3A. A lower resolution ADC is assumed: (A) 10-bit ADC; (8)8-bit ADC; (C) 6-bit ADC; (D) 4-bit ADC.
and are representative of the kinds of samples encountered in various chromatographic and electrophoretic systems. In most cases the intensity distribution was roughly Gaussian, with most data points clustered in a narrow range. We found that data collected with the 63-element mask could have a dynamic range of at least 7 bits for each element position. Data collected with the 127 and 255 active elements masks could have a dynamic range of at least 6 and 5 bits, respectively, at each element position. These findings are in agreement with eq 3.
CONCLUSIONS Although a complete characterization of Hadamard encoding instrumentation is complex, description of the major factors that limit the performance of a system is possible. An approximate characterization is sufficient to understand the present instrumentation and to guide future designs. Diffraction effects are negligible with the 100-pm mask used to measure the coherent transfer function of our system. However, diffraction will be increasingly important if smaller unit apertures are used in attempts to achieve higher spatial resolution. In fact, eq 4 predicts a cutoff frequency of 8 line-pairs/mm a t a width of 10 pm and a mask to surface distance of 2 cm. Achievement of high spatial resolution may require substantial redesign of the present system. Thermal effects for the modulation frequency range commonly used can be kept negligible. Our simple model predicts that the cut-off frequency for this contribution to the MTF ranges from 10 line-pairs/mm at 20 Hz to 62 line-pairs/mm at 800 Hz heating beam modulation for a glass or quartz substrate. Our model probably overestimates the effects of thermal diffusion, because we can find no measurable effect
of heating beam modulation frequency on the observed MTF. A better theoretical treatment of thermal diffusion contributions to MTF is needed, however. Motion blur is a major contributor to the observed MTF of our system, contributing a cutoff frequency of less than 5 line-pairs/mm. In principle, the motional contribution can be partially cancelled by use of a modified inverse transform (15) or by other standard approaches to image enhancement. The use of these computational procedures requires a constant velocity motor. In practice, incremental motion would eliminate this problem entirely at a similar or lower cost. With masks of unit aperture 25 pm or wider, the mask width itself becomes the resolution limiting factor. Our transfer function data clearly show this. Because the mask is used as a sampling window of width equal to the unit aperture width, the sampling theorem limits the spatial resolution of system to twice this width. In spatial frequency terms, at spatial frequencies for which the contrast is less than 0.5, aliasing will occur. For chromatographic applications, masks with 100200-pm unit aperture are adequate. The longest mask sequence for which Hadamard transform PDS is practical depends upon the dynamic range of the signal intensities. Commercial analog-to-digital converters with 16-bit resolution are widely available. It is unlikely that the primary signal transducers have a wider dynamic range. A 16-bit converter should allow operation of masks with 216 active resolution elements, allowing a 4-bit range for each element. In practice, mask runs of 1K-2K are all that are needed in a one-dimensional system. However, two-dimensional photothermal deflection or photoacoustic imaging with would require 16K-64K element masks. Such systems are possible.
Anal. Chem. 1087, 59, 1452-1457
1452
flection. Few solid samples are rugged enough to remain undamaged by tightly focused laser pulses. Many samples are damaged by exposure to tightly focused CW radiation. Hadamard encoding may extend the range of microscopy with other generally useful laser spectroscopies such as Raman spectroscopy. Experiments toward this goal are in progress.
LITERATURE CITED
2 W
ZUQ
2750
2SM
2-
MM
5lM
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MM
SIONAL INTENSIW (AQC u u n h )
I# 17 I#
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2150
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Flgure 6. (A) Distribution of data shown in Figure 3A; (B)Simulatlon of the distribution of the data taken from a sample approximating the configuration of the sample of the Figure 3A.
The major advantage of Hadamard encoding is that it allows acquisition of moderate to high spatial resolution spectroscopic information from an unfocused laser. The need to distribute laser power is not limited to transverse photothermal de-
(1) Morris, M. D.; Peck, K. Anal. Chem. 1988, 5 8 , 811A-822A. (2) Low, M. J. D.; Morterra. C. Appl. Spectrosc. 1984, 38, 807-812. (3) Coilette, T. W.; Parekh, N. J.; Griffin, J. H.; Carreira, L. A,; Rogers, L. B. Appl. Spectrosc. 1988, 40, 164-169. (4) Peck, K.; Fotiou, F. K.; Morris, M. D. Anal. Chem. 1985, 5 7 , 1359- 1362. ( 5 ) Wetsei, G. C.; McDonald, F. A. Appl. fhys. Left. 1982, 47, 926-928. (6) Lepoutre, F.; Fournier, D.; Boccara, A. C. J. Appl. fhys. 1985, 5 7 , 1009- 1015. (7) Benchikh, 0.; Fournier, D.; Boccara, A. C.; Teixeira, J. J . Phys. 1985, 4 , 727-731. (8) Jackson, W. B.; Amer, N. M.; Boccara, A. C.; Fournier, D. Appl. Opt. 1981, 20, 1333-1343. (9) Murphy, J. C.; Aamodt, L. C. J . Appl. fhys. 1980, 57, 4580-4588. (10) Coufal, H.; Moiler, U.; Schneider, S. Appl. Opt. 1982, 27. 116-120. (11) Coufal, H.; Moiler, U.; Schneider, S. Appl. Opt. 1982, 27, 2339-2343. (12) Fournier, D.; Lepoutre, F.; Boccara, A. C. J . fhys. Colloq. 1983, C6, 479-482. (13) Fotiou, F. K.; Morris, M. D. Appl. Spectrosc. 1988, 40, 704-706. (14) Fotiou, F. K.; Morris, M. D. Anal. Chem. 1987, 59, 185-189. (15) Harwit, M.; Sloane, N. J. A. Hadamard Transform Optics; Academic: New York, 1980. (16) Habibi, A,; Robinson, G. S. Computer 1974, 7 , 22-34. (17) Pratt, W. K.; Kane, J.; Andrews, H. C. R o c . I€€€ 1989, 5 7 , 58-68. (18) Pratt, W. K. IEEE Trans. Comrnun. Techno/. 1971, 79, 980-992. (19) Crowther, W. R.; Rader, C. M. Proc. I€€€, 1986, 5 4 , 1594-1595. (20) Goodman, J. W. Introduction to Fourler Optics; McGraw-Hili: New York, 1968. (21) Levi, L. Applied Optlcs; Wiley: New York, 1968. (22) Goodman, J. W. Stastistical Optics; Wiiey: New York, 1985; pp 36 1-688.
RECEIVED for review September 19, 1986. Resubmitted January 12,1987. Accepted February 11,1987. This work was supported in part by Grant GM37006 from the Public Health Service and in part by Grant CHE-8317861 from the National Science Foundation.
Peroxyoxalate Chemiluminescence Detection with Capillary Liquid Chromatography Andrew J. Weber and Mary Lynn Grayeski* Department of Chemistry, Seton Hall University, South Orange, New Jersey 07079
Peroxyoxalatechemlhmlnescence Is evaluated In a detectkn mode for packed captllary llquid chromatography. Relatively large volume flow cells (>1 ML) based on a sheathlng flow of chemlkmkrescent reagents around the column eftluent are evaluated In terms of sensltlvlty and band broadenlng. Because the postcolumn reagent flow ls large In proportlon to the total flow, the effluent condltlons have relatlvely llttle effect on the chemiluminescentslgnal over a wide range of organlc/aqueous solvent compos#lons. Detedon lhrlto In the femtomole range are posslble for certaln fluorophors.
The advantages of capillary liquid chromatography, including the potential for greater resolving power as a result 0003-2700/87/0359-1452$01.50/0
of increased column lengths and reduced solvent consumption, have recently been described in the literature (1-5). However, utilization of such columns requires the use of extremely small injection volumes and reduced detector cell volumes to reduce the contribution of extracolumn dead volumes. Fluorescence and UV detectors using submicroliter cell volumes (6-8) or on column detection (8-10) have been reported. Electrochemical techniques with reduced cell volumes have also been applied (11,12).However, these schemes require extremely small detection volumes with potential loss of sensitivity. Peroxyoxalate chemiluminescence (CL)has been demonstrated to be a sensitive and selective technique for the detection of suitable fluorophors in conventional (13-15) and microbore high-performance liquid chromatography (HPLC) (16). The increased sensitivity of CL over conventional @ 1987 American Chemical Soclety
