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ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
This research was supported by Contract No. AT(49-34) 0358 Nuclear Regulatory Commission, Contract No. from the U.S. EY-7643-02-2968 from the US.Department of Energy and
is part of a center program supported by Grant No. ES 00260 from the National Institute of Environmental Health Sciences and Grant No. CA 13343 from the National Cancer Institute.
Off-Axis Imaging for Improved Resolution and Spectral Intensities S. G. Salmon and J. A. Holcombe" Department of Chemistry, The University of Texas at Austin, Austin, Texas 78772
Optical systems for image transfer from source to spectrometer often employ on-axis refractive optics, i.e., lenses, because of the apparent ease in alignment and lens availability. Unfortunately, chromatic aberrations are inherent in any lens system, which can present several problems if image fidelity is required at different wavelengths. T h e focal length of a lens is generally specified by the manufacturer for the Na D line a t 589 nm. Using first-order approximations, the Gaussian formula readily shows the functional dependence of focal length on wavelength:
where f x is t h e focal length and nh is the index of refraction a t a specified wavelength, and rl and r2 are the radii of curvature of the respective surfaces. It follows that the focal length of a lens at different wavelengths can be determined by t h e ratio:
T h e implications on focusing are readily apparent. For example, a fused quartz lens with a nominal focal length of 15.0 cm will have a n actual focal length of 14.35 cm for t h e Cu resonance line a t 325 n m and 13.8 cm for the Zn resonance line a t 214 nm. It can be easily demonstrated that a system which is aligned to project an image on the spectrometer slit with unit magnification at 589 n m will result in grossly defocused images of the source at 325 and 214 nm. The lens could be moved to provide focused images on the entrance slit for each new wavelength, but the lateral magnification will not remain constant. For example, at 325 nm, a magnification of either 1.58 or 0.63 is available, while a t 214 nm, a magnification of 2.22 or 0.45 is obtainable by repositioning the lens t o place a focused image on the entrance slit. It should be recognized that the attainment of a focused image with unit magnification at any given wavelength can be achieved only by moving both the source and the lens, a task which is either difficult or impossible in most instances. T h e preceding discussion assumes the use of simple spherical lenses and is not intended to reflect the more expensive and complex optical configurations available which employ compound lens systems or achromats. Another difficulty encountered with refractive optical components is flare or internal reflection. While this can be minimized through use of coated lenses, the process is often expensive. Problems associated with chromatic aberrations and flare can be avoided by using reflective optics. However, this generally requires off-axis illumination which results in the appearance of higher order aberrations. For the application under discussion, the aberrations of astigmatism and coma are the main distortions t h a t need to be considered. Astigmatism, a higher order aberration, should be of particular 0003-2700/78/0350-17 14$0 1 .OO/O
concern and recently has been treated in excellent detail by Goldstein and Walters (I). When a spherical mirror is illuminated off-axis, two astigmatic images are formed. Closest to the mirror there is a line image perpendicular to the plane defined by t h e point object and the mirror normal which is referred to as the tangential image. The image farthest from t h e mirror is a line parallel to the incident plane and perpendicular to the tangential image which is referred to as the sagittal image. Located between the tangential and the sagittal images is the best approximation of a point image which is often referred to as the circle of least confusion. Mathematical equations for determining t h e positions and heights of the astigmatic images have been reported ( I ) . Pairs of mirrors have been used in various configurations to compensate for the off-axis aberrations and improve the image quality for spectrographic applications (I+). Astigmatic imaging through the use of an over-and-under, symmetric arm arrangement can be used t o an advantage when high quality spatial information is sought using photoelectric detection. An "over-and-under" configuration consists of the object point and the mirror normals lying in a vertical plane and results in a tangential image which is a horizontal line and a sagittal image which is a vertical line. A symmetric arm configuration consists of two mirrors being illuminated a t the same off-axis angle and corrects for coma. A diagram of the over-and-under, symmetric arm configuration showing the locations of the astigmatic images is given in Figure 1. T h e optical arrangement discussed in the paper is capable of optimizing both spatial resolution of the source and the detected spectral intensity. In addition, the chromatic aberration associated with refractive optics is eliminated. This is accomplished by employing the tangential and sagittal image planes to define the optimal vertical and horizontal foci, respectively in a symmetric arm, over-and-under, two-mirror system. EXPERIMENTAL Apparatus. A Jarrell-Ash 0.5-m Ebert monochromator equipped with a 1P28 multiplier phototube, a 100-pm entrance slit and 150-pm exit slit was used throughout. The photomultiplier tube output was capacitively filtered and measured with a digital multimeter. Spherical concave mirrors with approximate focal length of 800 mm were used in an over-and-under configuration in the foreoptics. Both a point light source (Oriel Corp.) and a 25-pm slit backlighted with a high intensity lamp were used in the object plane as test sources. Scanning slits of 25+m and 10-pm widths were used. Procedure. The mirrors were arranged in an over-and-under, symmetric arm configuration. The distance between the mirrors was 470 mm and the off-axis angle of illumination, Le., the angle between the incident beam and the mirror normal, was 5" for both mirrors. By placing the point source at the focal point of the first mirror, the reflected light was collimated and fully illuminated the second mirror. Under these conditions a separation of approximately 12 mm between the tangential and sagittal images was obtained. The distance from the second mirror to the monochromator entrance slit was approximately equal to the focal 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. l2, OCTOBER 1978
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Figure 1. Schematic of the over-and-under mirror configuration showing the point source, P; the mirror pair, M, and M,; and the relative locations of the tangential image, ST, at the scanning slit; the sagittal image, S., at t h e monochromator entrance slit; and the circle of least confusion, CLC
r Heighi l m m )
Source
++
Figure 3. Profile of the 25-pm source scanned with a 10-pm slit 3 c
"
==$== 0
b
C
Figure 4. Representation of aligning slits and images, (a) parallel pairs of slits on bhckened photographic plate, (b) image formed at the sagittal focus, and (c) image formed at tangential focus
Source
Height
imm)
Figure 2. Profile of the point source for the scan across (a)the tangential image and (b) the circle of least confusion length of the second mirror. The sagittal image was brought to a sharp focus on the entrance slit by fine adjustments in the distance between the point source and the first mirror. The 25-pm slit was mounted horizontally Le., parallel to the tangential image, on a XYZ translation stage equipped with a micrometer drive for vertical positioning. This slit was positioned so that the tangential image was brought to a sharp focus on it. The slit was then used to scan the tangential image of the point light source by taking intensity measurements every 25 pm. The 25-pm scan slit was then moved to the position of the circle of least confusion and the same scanning procedure repeated. Similar measurements were made using a backlighted Z - p m slit oriented horizontally in the object plane. In this instance a 10-pm scan slit was located near the monochromator and a measurement made for every 5 pm of vertical movement of the scan slit. RESULTS AND DISCUSSION T h e point source examined, like any real source, is not actually a point but has a finite area. When light from such a source is focused by a pair of mirrors, the astigmatic images formed are lines of finite width. For an over-and-under spherical mirror pair, the width of the tangential image line represents the height of t h e region being examined in the source. The profiles of the point source obtained by scanning the tangential image and circle of least confusion with the 25-pm slit are shown in Figure 2 . T h e halfwidths of the profiles were measured as 0.24 m m for the scan across the width of the tangential image and 0.55 mm for the scan across t h e circle of least confusion. Since both of these images are representations of the same region in the source, locating the scanning slit a t the tangential focus increases the apparent resolution by more than a factor of two. T h e manufacturer reports a nominal diameter of 0.18 m m for the point source
although it is believed that the measured 0.24-mm halfwidth is a better representation of the true diameter. The sharp rising and falling edges of the source profile taken a t the tangential focus suggest that the resolution of the system is better than 0.24 mm, the measured halfwidth of the point source. In attempts to determine the resolution, the experiment was repeated with a horizontal 25-pm slit backlighted by a tungsten filament lamp in place of the point source. With t h e sagittal image focused on the monochromator entrance slit, the tangential image was scanned with a 10-pm slit in 5-pm increments. T h e micrometers used for vertical translation required extrapolation between marked dial readings and could represent a significant error. In spite of this fact, the measurements were reproducible and conservatively indicate a resolution for the optical system of approximately 40 pm. A typical source profile with a measured halfwidth of 0.04 m m is shown in Figure 3. Figure 2 shows that an increase in intensity is also realized using the proposed arrangement. T o further verify this fact, the point light source was again placed in the object plane and the scanning slit was removed from the system. T h e circle of least confusion and the sagittal image were then focused on the monochromator entrance slit. T h e relative intensity measurements obtained at the sagittal image showed a 2.5-fold increase in intensity over that measured with the circle of least confusion focused on the entrance slit. The increase in spectral intensity when the tangential image is scanned with the spatial slit or when the sagittal image is focused on the monochromator entrance slit can be explained by the fact that the intensity of the image a t the circle of least confusion is less than a t either astigmatic focus. Since the total intensity of the point source is spread over a larger area at the circle of least confusion, a smaller fraction of the total available light passes through the slit and reaches the photomultiplier tube. This is true when the spatial and entrance slits are smaller than t h e image a t the circle of least confusion which is normally the case. T h e experimental results show that, when using reflective optics to eliminate the problem of chromatic aberration, the
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
astigmatism generated by off-axis illumination is not detrimental to the transfer of information from the source to a photoelectric detector. In fact, this aberration can be used to an advantage to increase spatial resolution and spectral intensities by proper focusing of t h e tangential and sagittal images on the spatial isolation aperture and entrance slit, respectively. Proper alignment and location of the images and spatial isolation aperture is a relatively simple task. Four lines as shown in Figure 4a are scratched on a small section of blackened photographic plate or smoked glass plate using a razor blade. The two line pairs should be perpendicular and as close to one another as possible. This plate is then located where the source of interest will be, e.g., on top of the burner for flame studies, and backlighted with a simple tungsten light bulb. T h e source is then moved until the sagittal image is on the monochromator entrance slit. T h e proper source position is obtained when the image of the parallel vertical
lines is resolved as shown in Figure 4b. The spatial slit is then positioned such that the image of the horizontal lines is most clearly resolved on this slit (Figure 4c). This alignment procedure has proved quite accurate in locating the proper position and, once again, is facilitated because of the lack of chromatic aberrations and, hence is applicable t o all wavelengths. LITERATURE CITED (1) S. A. Goldstein and J. P. Walters, Part I , Spectrochim. Acta, Part E , 31, 201 (1976), Part 11, Spectrochim. Acta, Part E , 31, 295 (1976). R . D. Sacks and J. A. Holcombe, Appl. Spectrosc., 28, 518 (1974). L. C. McGonagle and J. A. Holcombe, Appl. Spectrosc., in press. J. P Walters. Anal. Chem., 40, 1540 (1968). J. P. Walters and S. A. Goldstein, ASTM STP 540, American Society for Testing and Materials, 1973, pp 45-71. (6) R. J. Klueppel, D. M. Coleman, W. S. Eaton, S. A. Goklstein, R. D. Sacks, and J. P. Walters, Spectrochim. Acta, Part B , 33, 1 (1978).
(2) (3) (4) (5)
RECEIVED for review April 13, 1978. Accepted June 13, 1978.
Determination of Phosphorus-Containing Compounds by Spectrophotometry Alasdair M. Cook,* Christian G. Daughton, and Martin Alexander Laboratory of Soil Microbiology, Department of Agronomy, Cornel1 University, Ithaca, New York 14853
No single method has been applicable for the determination of total phosphorus in the large spectrum of naturally-occurring and synthetic phosphorus-containing compounds, especially for those of extreme stability; e.g., ionic 0,O-dialkyl phosphates and 0-alkyl alkylphosphonates; the available phosphorus assay procedures determine only certain classes of phosphorus compounds. Phosphate esters from cells and tissues have been assayed routinely for total phosphorus after acid hydrolysis (e.g., 1). Nonesterified alkylphosphonates have been determined after alkaline persulfate oxidation ( 2 ) ; however, 0-alkyl alkylphosphonates are not hydrolyzed quantitatively ( 3 ) ,and the detection limit and the sensitivity in these determinations are poor (30-1600 nmol/assay). We have found (Cook and Daughton, unpublished data) that dry ashing with 5 M "OB ( 4 ) results in incomplete and erratic recovery of dihydrogen 2-aminoethylphosphonate as orthophosphate. Subsequently, we found that a published method for wet ashing of aminoalkylphosphonates ( 5 ) could be extended and modified to give a simple, safe, general procedure for nongaseous phosphorus compounds in the 1-50 nmol range: this new procedure is described here. T h e orthophosphate resulting from the ashing was assayed by the highly sensitive method of Bartlett ( I ) . EXPERIMENTAL Apparatus. Wet ashing was done with a fluidized sandbath (Tecam SBL-1, Techne Inc., Princeton, N.J.). (Caution: All ashing must be done in a fume hood equipped with a safety screen.) The bath was fluidized with compressed air (3 psig) precleaned of oil and water. Samples were ashed in 20 x 150 mm screwcap Pyrex tubes held in a circular 25-place stainless-steel rack. A simple accessory was constructed to allow easy placement and removal of the rack from the bath and to prevent sand overflow and contamination of the samples. An aluminum cake pan (22-cm base, 26.5-cm diameter top, 18 cm deep) with a 17-cm diameter hole in the base held two horizontal bars through its side, 2 cm from the base, and the rack was suspended on the bars. This assembly seated firmly on the inside lip of the bath. An aluminum plate (30-cm diameter) with 20-mm holes was designed to slide over the tops of the tubes and rest on the pan 2 cm below the tube tops. A dial thermometer (range 0-250 " C ) was used to measure temperature. 0003-2700/78/0350-1716$01,00/0
Absorbance values were measured with a Spectronic 88 spectrophotometer (Bausch & Lomb, Rochester, N.Y.) equipped with a micro flow-through cell of 1-cm path length. Calibrated Gilson automatic pipets were used except where indicated. All glassware was cleaned with nitric acid to eliminate contaminative phosphate ( 6 ) . The acid digestion mixture contained 0.75 mol HC104,1.0 mol H2S04and 10.5 mol H N 0 3 in 1 L deionized distilled water as in (5). (Important: Mix in the following order: H20,H2SO4,HN03, and HClO,.) The ammonium molybdate solution was 10 mM in water. The Fiske-SubbaRow reagent contained 0.79 mol NaHS03, acid, and 40 mmol Na2S03 10 mmol l-amino-2-naphthol-4-sulfonic in 1 L distilled water ( 2 ) . Ashing a n d Assay Procedures. Standards were prepared in either water or buffered salts solution (6). Biological samples (e.g., from bacterial cultures) were filtered through membranes of 0.2-gm pore diameter to allow for analysis of the cell-free fluid. Samples (1.00 mL) were measured into the ashing tubes, and 1.50 mL of digestion acid was added by Dispensette (Brinkmann Instruments 1nc.i to each tube. The fluidized bath was brought to 80 O C , and the samples were placed therein. The temperature was increased at 10 OC/min to 225-230 "C for 1-1.25 h (the final temperature could be maintained for at least 2.5 h) after which the samples were removed. (Note: The air pressure should be decreased during warming of the bath to prevent excessive fluidization.) Loss of phosphorus compounds suspected to be volatile (e.g., 8% with dimethyl methylphosphonate) was eliminated by preincubation (30 min) with the acid-digestion mixture in capped tubes at 80 " C ; the caps were then removed, and the standard ashing procedure was followed. A t the end of the ashing, the H2S04(1.5 mmol, 100 wL)remained in each tube. When the tubes reached ambient temperature, 0.86 mL of ammonium molybdate and 40 pL of Fiske-SubbaRow reagent were added. The tubes were sealed with Teflon-lined caps, heated at 100 "C for 10 min, cooled, and mixed, and the absorbance at 830 nm was read against water. Chemicals. Dimethyl hydrogen phosphate (DMP) was obtained from Pfaltz & Bauer (Stamford, Conn.). Diethyl hydrogen phosphate (DEP) was purchased from Eastman Organic Chemical Div. (Rochester, N.Y.). Dimethyl methylphosphonate (DMMPn) was purchased from Aldrich Chemical Co. (Metuchen, N.J.). The potassium salts of 0,O-dimethyl and 0,O-diethyl phosphorothioate and 0,O-dimethyl and 0,O-diethyl phosphorodithioate (DMTP, DETP, DMDTP, and DEDTP, respectively) were generous gifts of American Cyanamid Co. (Princeton, N.J.). The potassium salt
a 1978 American Chemical Society
