Improving long-path differential optical absorption spectroscopy with a quartz-fiber mode mixer

Transcription

1 Improving long-path differential optical absorption spectroscopy with a quartz-fiber mode mixer Jochen Stutz and Ulrich Platt Long-path differential optical absorption spectroscopy DOAS has become an increasingly important method for determination of the concentration of tropospheric trace gases e.g., O 3,NO 2, BrO, ClO. The use of photodiode array PDA detectors enhances long-path DOAS systems considerably owing to PDA s higher sensitivity resulting from the multiplex advantage. The detection limits of these systems are expected to be 1 order of magnitude lower than systems of similar optical setup with scanning detectors. When the scanning detector is simply replaced by a PDA, unwanted spectral structures of as much as appear. The size of these randomly changing structures exceeds the photon noise level by 2 3 orders of magnitude thus severely limiting the sensitivity. We show that an angular dependence of the response of the PDA causes this structure in combination with unavoidable changes in the illumination. A quartz-fiber mode mixer, which makes the illumination of the spectrograph detector system nearly independent of the angular intensity distribution of the measured light, was developed and tested. This new device reduces the unwanted structures in laboratory and field experiments by a factor of 10. The detection limits of long-path DOAS instruments with PDA detectors are improved by the same amount and are thus lower than those of currently used systems with scanning detectors. At the same time a much shorter measurement time by 1 order of magnitude becomes possible Optical Society of America Key words: Differential optical absorption spectroscopy, quartz fibers, measurement techniques. The authors are with the Institut für Umweltphysik, University of Heidelberg, INF366, D Heidelberg, Germany. J. Stutz is currently with the Department of Chemistry, University of California, Irvine, Irvine, California Received 4 March 1996; revised manuscript received 12 August $ Optical Society of America 1. Introduction Since its first applications in the late 1970 s 1 3 differential optical absorption spectroscopy DOAS has developed into a widely used method for the detection of tropospheric trace gases. DOAS is based on the measurement and analysis of absorption spectra in the atmosphere. The absorption path is situated in the open atmosphere, with a typical length of 100 m to several kilometers. Because extinction processes such as Rayleigh scattering and Mie scattering show interferences with the trace gas absorptions, the classic approach of absorption spectroscopy cannot be used in this application. The principle of DOAS is the separation of the trace gas absorption cross section into two parts: B that varies slowly with wavelength and a quickly varying differential cross section : B. As the spectral characteristics of the aerosol extinction processes vary slowly with wavelength, DOAS analyses only narrow absorption bands with a width of less than 5 nm. The separation of can be performed by filter techniques described, for example, in an extensive review of DOAS technique published elsewhere. 4 The main advantage of DOAS is its ability to detect absolute trace gas concentrations without calibration if the absorption cross sections are known. Because the absorption path is located in the open atmosphere, DOAS gives direct insight into the chemical processes; in addition the trace gas concentrations are not influenced by the measurement. Therefore DOAS is especially useful for the detection of highly reactive trace gases. Several tropospheric trace gases were identified for the first time with DOAS, that is, NO 3, 3 OH, 1 HONO, 2 BrO, 5,6 and ClO. 6 Many other trace gases, i.e., ozone, NO, NO 2, HCHO, SO 2, and aromatics, have been measured. DOAS can also be used for the 20 February 1997 Vol. 36, No. 6 APPLIED OPTICS 1105

2 detection of stratospheric trace gases i.e. O 3,NO 2, OClO, BrO. 7 One can perform the analysis of atmospheric absorption spectra by modeling the spectra numerically. 4,8 11 Frequently several species show overlapping absorptions in the same wavelength interval; therefore the model that describes the measured spectrum consists of a linear combination of the differential cross section of these trace gases. 11 One can calculate the size of the absorption structures by a fitting procedure that scales the cross sections. The derived scaling parameters are then used to calculate the trace gas concentrations. The separation of the absorption structures is possible because every trace species has a unique cross section that can be used to identify a species similar to the identification of a fingerprint. Experiments showed that this identification and the derivation of the concentration with the model and the fitting procedure is possible even at noise levels that exceed the amplitude of the absorption structures. 11 The difference between the measured spectrum and the model is usually called a residual or a residual spectrum. This residual contains all the structures that are not explained by the model, for example, noise, instrumental structures, and unknown absorbers. The size of the residuals defines the detection limit of DOAS instruments because only absorption structures larger than approximately 1 3 of the residuals can be detected reliably. The original tropospheric DOAS instrumental setup developed by Platt et al. 4,12 consists of a lamp and a collimating telescope at one end of the absorption path. The transmitted light beam is received after its path through the atmosphere by a Newtonian telescope at the other end of the path, with the light focused on the entrance slit of a grating spectrograph. Modern DOAS systems make use of retroreflectors at one end of the absorption path to double the length. 5,13 These systems are adjusted more easily because the sending and receiving telescope is placed at one end of the light path, with only passive components placed at the other. Although scanning monochromators have been used in the past to record the absorption spectrum, 14 the major problem of these systems is the correction of rapid intensity changes caused by atmospheric turbulence, referred to as scintillation noise. To overcome this problem, Platt et al. 12 fed the light into a spectrograph and used a slit that rapidly scanned over a section of the spectrum and a photomultiplier as detector. Because of the arrangement of the slits on a rotating disk this detector is called a slotted disk SD detector. 2,12 Typical system measurement times are 20 min on a 5-km light path. After atmospheric spectra are evaluated by the removal of all trace gas absorptions, residual structures of typically remain. These residual structures are caused mainly by the statistical photon noise, which indicates that the method is limited by the available light intensity. The use of a photodiode array PDA detector, which replaces the SD detector, should improve the detection limit. 4,9,15 The PDA records all the wavelengths in the observed interval simultaneously and thus also overcomes the problem of scintillation noise. Compared with scanning systems of similar optical setup, the PDA collects times more photons in the same time interval. Because this multiplex advantage of the PDA reduces photon noise by a factor of more than 10, a corresponding improvement of the detection limit is expected. In contrast with the SD detector, the PDA requires correction of the pixel response, which varies as much as 1% over the array. This can be achieved by dividing the measured spectrum by a spectrum of a sufficiently smooth light source, i.e. a tungsten lamp. Another approach to correct the pixel response is the scanning multichannel technique described by Knoll et al. 16 This method was extended by Brauers et al. 17 for atmospheric measurements. While the described methods of pixel response correction give satisfactory results in laboratory and stratospheric measurements, there are unfortunately further problems with diode array detectors in tropospheric DOAS instruments with artificial light sources. Random residual structures of peak to peak or are found after atmospheric absorption spectra are evaluated. These structures exceed by far the expected photon noise and the residual structures found with the SD instruments. The detection limit of these naive PDA systems limited by the magnitude of the residual structures is therefore a factor of 10 higher compared with the SD instruments. Here we present laboratory measurements showing that an angular dependence of the detector response causes these structures, and we discuss the different processes leading to this dependence. We describe a newly developed quartz-fiber mode mixer, which makes the illumination of the PDA independent of the angular intensity distribution of the measured light and thus greatly reduces these residual structures. The quartz-fiber mode mixer was tested in a series of atmospheric measurements of O 3,NO 2, SO 2, and HCHO. 2. Laboratory Experiments A. Experiment To investigate the problems with the PDA during atmospheric measurements, we performed experiments to reproduce the effect in the laboratory. Figure 1 shows the experimental setup. Light of a commercial tungsten bulb with a stabilized power supply was collimated by two f 100-mm lenses and a 200- m pinhole. This beam was then focused by another f 100-mm lens on the entrance slit of the spectrograph. The focal spot of 250- m diameter was of a size comparable to the image of the light source on the entrance slit during the atmospheric measurements performed in Heidelberg see below. In all the experiments we used an f 6.9 Czerny Turner spectrograph Acton Spectra Pro 500 with a 1106 APPLIED OPTICS Vol. 36, No February 1997

3 Fig. 1. Experimental setup to investigate the dependence of the spectrograph detector system on the illumination. The aperture stops A, B, C, and D are inserted into the collimated light beam, which is produced by two lenses and a 200- m pinhole. The light is focused on the entrance slit of the spectrograph by another lens. focal length of 500 mm. The spectrograph was equipped with a 1200-groove mm grating, giving a dispersion of approximately nm pixel or 1.5 nm mm. The entrance slit was adjusted to a 200- m width by a 200- m height, which matched approximately the size of the focal spot on the entrance slit. The astigmatism of the spectrograph caused the height of the image of the entrance slit in the focal plane to increase to approximately mm; therefore the height of the PDA detector see below was almost completely illuminated. The spectrograph was thermostated at C to achieve maximum spectral stability of the instrument. Baffles inside the spectrograph blocked reentrant light from the grating, thus reducing the stray light to less than 1% of the measured light intensity. The laboratory measurements were performed in the spectral interval from 530 to 570 nm. The detector, based on an EG&G Reticon RL1024SR random access photodiode array 18 with 1024 diodes and the associated readout electronics, was built in our institute. 15 The photodiodes have a center-to-center spacing of 25 m and a height of 2.5 mm 1:100 aspect ratio. For the laboratory measurements we used a PDA with a SiO 2 protective layer of 3- m nominal thickness m calculated thickness 15. In the atmospheric experiments described below we changed to a PDA of the same type with a protective layer 1 m thick. Interferences in these protective layers introduce sinusoidal structures of as much as 10% amplitude in the response of both diode arrays. 19 However, the thinner SiO 2 layer increases the spatial wavelength of the sinusoidal Fabry Perot étalon structure compared with the PDA with the 3- m layer. The larger spatial wavelength reduces problems with the étalon structure that are caused by illumination changes and the growth of the layer by the condensation of gases during the operation of a cooled PDA. 15 The arrays are used without the protecting quartz window that is normally fixed to the semiconductor housing. This eliminates stray light caused by reflection at this window. 20 To reduce dark current, we cooled the PDA in the detector to 35 C 0.1 C by a three-stage Peltier cascade on a fan-cooled heat sink. With typical exposure times of 1sinourmeasure- ments, this temperature was sufficiently low to reduce the dark current contribution to the signal below , making a correction unnecessary. The detector is filled with argon at atmospheric pressure to reduce the rate of diffusion of gases onto the PDA, and thus the change in the étalon structure. 15,19 The electronics of the detector are based on a chargesensitive preamplifier, an integrator and a 16-bit analog digital converter. The instrument is controlled by a PC running the program MFC, 21 which is also used for storage and analysis of the recorded spectra. To change the illumination of the spectrograph and the diode array detector in a defined and reproducible way, we inserted four different aperture stops in the collimated light beam as illustrated in Fig. 1. The aperture stops C and D were designed to simulate the behavior of a Newtonian telescope, with a secondary mirror blocking the center part of the light beam. All the spectra recorded in the experiment were corrected for electronic offset and background light, which was measured by blocking the light beam. The spectra, S A, S B, S C, S D, recorded with the aperture stops A, B, C, and D were compared with a spectrum S 0 without an aperture stop by calculating the ratios S A S 0, S B S 0, S C S 0, S D S 0. To determine the noise during measurements, we measured all the spectra twice, i.e., S 0 and S 0. The ratios, i.e., S 0 S 0, S A S A, were pure noise spectra see top of Fig. 2. Because only narrow structures are of interest for the DOAS evaluation, we removed any broad structures by dividing the quotient spectra by a fitted fifth-degree polynomial. 12 We performed all measurements by adding 100 readouts of the PDA with an exposure time typically 1 s adapted to reach a diode saturation of 50%. A larger number of readouts did not change the results described below, but they reduced the noise level of the ratios. A correction of the diode response was not necessary because two spectra measured with the same detector were divided. The division by a tungsten lamp spectrum is, in fact, the procedure normally used to correct the diode response nonuniformity in DOAS measurements as described above. Figure 2 shows the results of the experiments with a PDA with a 3- m SiO 2 layer. To emphasize the narrow structures, we plotted only pixels The remainder of the spectrum has a similar appearance. The top spectrum is a lamp spectrum S 0 without an aperture stop. The spectrum shows the typical sinusoidal étalon structure of approximately 10% amplitude. The average intensity was BU the sum of 100 readouts of the diode array, where one binary unit BU corresponds to approximately 1000 photoelectrons in a diode. The noise spectrum S 0 S 0 shows no evidence for any spectral structure not caused by photon noise or detector noise. The noise during the experiments was below peak to peak or see Fig. 2. The division of two 20 February 1997 Vol. 36, No. 6 APPLIED OPTICS 1107

4 spectra taken with the same aperture stop also resulted in pure noise spectra with the same peak-topeak amplitude. The ratios of the spectra with and without aperture stops, i.e., S A S 0, show spectral structures larger by a factor of 5 20 compared with the pure noise spectrum S 0 S 0. The smallest structures are found in S C S 0 with , which is not surprising because the change of the illumination is small compared with the other aperture stops. S D S 0, in contrast, shows the strongest structures. In this case the change in illumination, especially in the angular intensity distribution, is large. All the quotient spectra show their strongest structures around pixels 130 and 400; the smallest structures are found around pixel 250. The structures of the quotient spectra S A S 0 and S B S 0 are approximately the same size and are anticorrelated to each other over a large part of the spectrum. This anticorrelation may be caused by the specific shape of the aperture stops. With aperture stop B only the light from the left half of the beam is measured. The structures displayed in Fig. 2 are thus produced by a change of illumination in the horizontal direction. Aperture stop A blocks all the light except for the lower right quarter of the beam. When only the horizontal direction is considered, the change of illumination is opposite that of aperture stop B and thus produces the inverse structure in the spectra. Other differences are probably caused by the illumination change in the vertical direction as discussed below. Similar experiments performed with a SD detector did not show structures of comparable size; therefore the reported problems are caused by the PDA detector. We conclude from the laboratory experiments described in this subsection that a change in the angular intensity distribution of the light entering the spectrograph leads to the spectral structures found in the experiments. It is therefore crucial for DOAS measurements to guarantee a constant illumination of the spectrograph aperture and the diode array. Fig. 2. Structures produced by changes in illumination of the spectrograph detector system. The top spectrum shows a typical lamp spectrum with its sinusoidal étalon structure. The noise level in the ratio of two spectra taken under identical conditions without aperture stop S 0 S 0 is lower than the spectral structures found in the ratios of spectra taken with different illuminations i.e., aperture stops A D inserted, S A S 0, S B S 0, S C S 0, and S D S 0. The y scale of S D S 0 was changed to show the complete spectrum. The aperture stops used to change the illuminations are shown in Fig. 1. B. Causes of Photodiode Array Structures We present three possible explanations for illumination effects on PDA s: dust on the PDA, an irregular protective SiO 2 layer on the PDA, and angular dependence of the diode sensitivity. It is difficult to separate these effects in the measurements; therefore we performed model calculations to estimate the size of the structures caused by the various effects. In the following we discuss the results of the model calculations. 1. Dust on the Photodiode Array A common problem when one uses a PDA without the protecting quartz window on the chip housing is dust particles on the semiconductor surface. Even though the detectors are probably carefully assembled in a clean room, particles are often found on the PDA. If the particles are large enough, they can be easily identified in the response curve of the diode array. The largest differences usually found in the response of the detectors are between 0.5% and 1%. If completely opaque particles are assumed, their area on one diode can be estimated to be smaller than 500 m 2. To explain the dependence on illumination, for example, by a shadow of the particle, it is necessary to take into account the height of the particle. Figure 3 illustrates the principle of this mechanism. We assumed a dust particle with a rectangular cross section placed directly on the protective SiO 2 layer. In Fig. 3 a the PDA is illuminated with light coming from a cone, which corresponds to measurements without an aperture stop. On the right the particle 1108 APPLIED OPTICS Vol. 36, No February 1997

5 the presence of a dust particle this intensity reduction is smaller, because the additional shadow on the right side of the particle reduces the intensity only in the case without an aperture stop see Fig. 3 a. We performed our calculations based on this simple one-dimensional model for different sizes of particles by comparing the calculated intensities for full illumination without aperture stop, Fig. 3 a and with illumination of half of the aperture cone aperture stop B, Fig. 3 b. The f-number of the illumination geometry was f 6.9, which is equal to the value of the spectrograph used in the laboratory experiments described above. Assuming a particle length of 50 m parallel to the long side of the diode, a width of 10 m perpendicular to the diode, and a height of 40 m, we derived a residual structure of when changing from full illumination to aperture stop B. The structure increases nearly linearly with the height and the length of the dust particle. Values of , as were found in the experiments see Fig. 2, can be explained if the length of the particle is increased to 100 m and the height to 60 m, always with the assumption that only one single particle is found on the diode. The structures do not depend on the particle width as long as a shadow is produced on one side of the particle. However a width comparable with the height would appear reasonable and thus lead to a total area of the particle of 6000 m 2. The results of the calculation suggest that particles are probably not the cause of the observed residual structures since particles of the necessary size would cause a much larger variation of the detector response than the observed 1%. Fig. 3. Effects that give rise to illumination-sensitive response of the diode of a PDA: a, a dust particle illustrated with a rectangular cross section throws a shadow on the diode on the right of the particle. The diode is illuminated by a full cone of light i.e., no aperture stop present ; b, if only the right half of the cone is illuminated e.g., owing to the presence of aperture stop A or B the shadow is not present; c, d, an irregular surface changes the interferences in the protective layer of the PDA. The figure explains the model calculations performed to investigate this effect in two dimensions: A ray enters the layers on the PDA with angles ; the light path in the layer is therefore longer compared with a vertical ray; as a cone of light is thrown from the focusing mirror of the spectrograph on the PDA, the intensity must be integrated over all angles to derive the total intensity I tot. blocks the left part of the cone and casts a shadow on the diode. For small angles, as in our case, the intensity integrated over this part of the shadow is lower by 25% compared with the same area without shadow. Figure 3 b shows the same situation with only the right half of the light cone illuminated, as with aperture stop B. The shadow on the right side of the dust particle is missing. In the case without dust particles, the intensity reduction that is due to aperture stop B is 1 2. In 2. Differences of the Étalon Structure Resulting from Surface Irregularities Interferences in the protecting SiO 2 layer have a strong influence on the response of the diode array, resulting in a broad sinusoidal structure usually called a Fabry Perot étalon structure see top spectrum in Fig. 2. The étalon is produced by two thin layers on the semiconductor, forming the diode array: one layer of SiO 2 index of refraction n with a thickness of approximately 3 m protecting the semiconductor and a second layer, probably of condensed gases index of refraction n 2 1.3, with a thickness of approximately 0.5 m Fig. 3 d. Interferences in these two layers explain the broadband étalon structures in the response of the diode array. 15 Since the light path length in the layers and thus the interferences depend on the angle of the light incident on the PDA, the étalon structure depends on the angular intensity distribution of the measured light. We attempted to simulate theoretically the observed effects shown in Fig. 2 by expanding the model described by Stutz and Platt, 15 assuming an irregular thickness of the second layer in the model. If the variation in the response of the diodes of less than 1% would be due to only the change of the thickness, a variation of less than m over the diode array would be required. 20 February 1997 Vol. 36, No. 6 APPLIED OPTICS 1109

6 The intensity I of a light beam, here with an intensity I 0 1, detected by the PDA can be described by the interference of three different light paths in the two layers: I,, 1 R 1 R cos 2 1, R 2 R cos 2 2, R 3 R 1 R cos 2 1, 2,. The R i are the reflectivities at the three boundary layers R , R , R , assuming n 1 1, n 2 1.3, n 3 1.6, n semic The i are the light path lengths in the two layers; they depend on the refractive index of the layers n i and the entrance angles and parallel and perpendicular to the plane of the spectrograph. The values of the light path lengths i were calculated considering these entrance angles, the thickness of the layers d i, and the refractive indices n i : (1) i, 2 n i d i cos cos. (2) To simulate the illumination of the PDA, we integrated the intensity I,, over a range of angles and : max max I tot I,, d d. (3) min min The angles were chosen in the range 4, which corresponds to the geometry of our f 6.9 spectrograph. We also assumed that the PDA is rotated with respect to the focusing mirror of the spectrograph with angles PDA and PDA Fig. 3 c. The rotation of PDA 6 in the plane of the spectrograph Fig. 3 c is given by the super-flat-field condition for the focal plane of the spectrograph. 22 A rotation in other directions can be caused by an erroneous adjustment of the spectrograph PDA system. The adjustment of this rotation is difficult, because the influence on the width of a spectral line is small, i.e. PDA 5 would cause a broadening of a spectral line of less than 0.3 pixels. For the model calculations we assumed a smaller value of PDA 3. The thickness d 1 of layer 1 was assumed to vary from to m with an average of 0.67 m 15 Fig. 4. On the basis of earlier calculations 15 we assumed a fixed thickness of d m for layer 2. The spectra were calculated for a dispersion of 570 nm 0.04 nm pixel i, where i denotes the pixel number. We simulated spectra S th 0 for S 0 without aperture stop and S th A, S th B, and S th D for the aperture stops A, B, and D. To visualize the response of the diodes, we divided S th 0 by a fitted polynomial to remove any Fig. 4. Result of the model calculation of structures introduced by an irregular protective layer surface with a thickness d 1 of the first layer. The second layer was assumed to be m thick. The model calculations were performed for aperture stops A, B, and D. S th A S th 0, S th B S th 0 and S th D S th 0 show the quotient spectra after they are divided by a fitted polynomial. broad structures. The calculated peak-to-peak variation in S th 0 is of the order of Fig. 4, similar to the value found in the experiments. In a manner similar to the experiments we calculated S th A S th 0, S th B S th 0, and S th D S th 0 and divided these ratios by a fitted polynomial. The amplitude of the structures of S th A S th 0 and S th B S th 0 in Fig. 4, of peak to peak, was comparable with the size found in the experiments. Also the anticorrelation of the structures described above was reproduced. The variation in S th D S th 0 is smaller than in the corresponding spectrum in the experiment and shows an anticorrelation with S th A S th 0. The strong structures near pixels 360 and 410 in S D S 0 could not be reproduced by the model and probably have a different cause. The model shows that for a diode array with a SiO 2 layer thickness of 1 m, the surface irregularities have to be approximately a factor of 2 3 larger than in the case of a 3- m-thick layer to explain a similar structure size APPLIED OPTICS Vol. 36, No February 1997

7 Table 1. Peak-to-Peak Residual Structures for Various Illuminations Measured in the Laboratory a Aperture Stop A B C D Intensity Loss % Without Diffuser Diffuser Diffuser Diffuser Mode Mixer a Diffuser 1 Optilas 10 diffuser, diffuser 2 Spindler & Hoyer quartz diffuser, and diffuser 3 weighing paper were placed directly in front of the entrance slit of the spectrograph. 3. Angular Dependence of the Diode Sensitivity Another explanation would be a different angular dependence of the sensitivity of individual diodes caused, for example, by errors in the production process of the PDA. Because no information on the angular sensitivity of the photodiodes is available, an estimation of this effect is not possible. The model calculations clearly show that an irregular layer thickness on the PDA can be used to explain the angular dependence of the diode array response, but the simulation for aperture stop D indicated that other unknown processes could also play an important role. We therefore conclude that a combination of several effects causes the angular dependence of the response. 3. Quartz-Fiber Mode Mixer The experimental and theoretical results described above show that the dependence of the diode array response on the angular intensity distribution causes the residual structures found in tropospheric DOAS applications with artificial light sources. One way to solve this problem is to use optical components that make the illumination of the spectrograph detector system more uniform. Our first approach was to use diffusers see Table 1 that were mounted directly in front of the spectrograph entrance slit or between two lenses in the collimated light beam. 23,24 The first lens focused the light on the diffuser; the second lens collimated the diffuse light coming from the diffuser. Both setups gave approximately the same results. We compared the peak-to-peak difference of the spectral structures of the ratio S A S 0 with the different diffusers. The structures of the quotient spectra are lower by approximately a factor of 2 4 see Table 1 compared with the results without a diffuser. The smallest structures could be achieved with diffuser 3. Even with the diffuser the structures are higher than the noise level by a factor of 3. The disadvantage of diffusers is the large loss of light intensity 50 75% and higher that reduces the multiplex advantage of the PDA. We therefore searched for a different optical device with the ability to diffuse light better at smaller intensity loss. A. Quartz Fibers Quartz fibers are now widely used in spectroscopy, for example, to transmit light into a spectrometer without complicated optical systems. For DOAS measurements that observe relatively wide spectral regions we used multimode fibers, the properties of which were investigated in the 1970 s mostly in light of their use in communication techniques. 25 The behavior of multimode fibers showed that mode coupling caused by microbending and imperfections in the refractive-index distribution and the geometry of the waveguide was responsible for additional intensity loss in the fiber. On the other hand, mode coupling was beneficial for reducing the delay distortion of optical signals that results from uncoupled multimode operation. 25 To introduce mode coupling, mode scramblers or mode mixers based on microbending the fiber were used. 26 To build a diffusing device to reduce the illumination effects described above, we investigated mode coupling in the multimode quartz fibers used for DOAS measurements. We used bare step-index quartz fibers of a diameter of 200 m and a numerical aperture of 0.12 BTO Bungert, Germany. To keep unwanted external light from entering the fiber through the cladding, parts of the fiber were shielded by a flexible black plastic tube. B. Experiment Figure 5 shows the experimental setup for the investigation of the mode mixing in quartz fibers. Light of a standard helium neon laser is fed into the fiber. The laser can be rotated with respect to the fiber axis with an angle to excite different modes in the fiber. Fig. 5. Experimental setup to investigate mode coupling in a multimode quartz fiber. The light beam of a helium neon laser is fed into the fiber at an angle. The fiber is placed between two plates with a step profile. A sheet of rubber is placed between the top aluminum plate and the profile to protect the fiber. The plates can be pressed together with a force F to introduce microbending to the fiber. The light intensity leaving the fiber is measured with a photoresistor on a screen at a 15-cm distance from the fiber end along the X axis. 20 February 1997 Vol. 36, No. 6 APPLIED OPTICS 1111

8 Fig. 7. The quartz-fiber mode mixer developed for field experiments. The quartz fiber has a length of 2 m. To shield the bare fiber from unwanted stray light, the mode mixer was installed in a closed aluminum box 15 cm 10 cm 10 cm and the parts of the fiber outside this box were fed through a flexible black plastic tube. The fiber has a numerical aperture of The fan causes gentle irregular bending of the fiber, thus averaging over different mechanical conditions of the fiber, which can change with temperature. Fig. 6. Angular intensity distribution at the fiber end. The distribution depends on the force on the mode mixer: a, b, at a force of F 1.7 N a nearly uniform distribution can be reached for the entrance angle 8 ; c, the dependence of the angular intensity distribution for various. The shape of the distribution is approximately constant, independent of. The fiber is fixed between two aluminum blocks with a profile as shown in Fig. 5. A sheet of rubber was placed between the aluminum blocks and the profile to avoid damaging the fiber at high pressures. The two blocks were pressed together with a force F by placing different weights on the upper block. The weight of the thin upper aluminum block was included in the determination of the force on the fiber. The light leaving the fiber illuminates a screen at a 15-cm distance, where its intensity is recorded by a photodetector. The intensity values were measured along a line X through the center of the image. Figure 6 shows how the intensity distribution changes for different forces on the fiber. The effect for an entrance angle of 0 and 8 is given in Figs. 6 a and 6 b. In Fig. 6 b the shape of the intensity distribution changes from a ring at F 0N to a nearly uniformly circular distribution at a force of approximately F 1.7 N. Higher pressures do not change the intensity distribution any further. For 0 the changes are only small. We used the data of 0 to investigate the change in the total intensity transmitted through the fiber by integrating the intensity over the image. The intensity is reduced by approximately 10% for the higher pressures. In addition, the fiber loses 10% intensity owing to reflection at its ends and extinction in the fiber. We used these results to adjust the pressure for optimal mixing without losing too much intensity. We chose a force of 1.7 N. To investigate the uniformity of the far-field image, we changed the entrance angle. The measured intensity distribution is shown in Fig. 6 c. The uncertainty of the intensity entering the fiber was approximately 10%. All the intensity distributions show a similar shape independent of. Because 8 is already close to the total reflection limit of the fiber, the intensity is much lower. This experiment showed that the mode mixer can be used to produce a uniform intensity distribution at its exit, independent of the distribution at the entrance. The intensity loss of the mode mixer is 20%. We also tested the behavior of a mode mixer in spectroscopic measurements with the same tests as described above. The setup described in Fig. 1 was extended by the addition of a quartzfiber mode mixer between the second lens and the spectrograph. The fiber exit was placed at the position of the spectrograph entrance slit. For this test we used a 10-m-long fiber with a mode mixer near one end. The first experiments showed that the fiber itself produced structures owing to temperature changes and mechanical changes between two measurements. To reduce this effect, we included a turbulent air stream produced by a fan shaking the fiber randomly to average over the different mechanical conditions Fig. 7. This increased the stability and reproducibility of the measurements considerably. In a manner similar to the experiments described above, we compared spectra measured with and without aperture stops. These tests were performed only with aperture stops A and D because they showed the largest residual structures. The number of scans was increased to 400 to reduce the noise and to visualize the residual better. Figure 8 shows the quotient of the spectra after we removed broad structures by dividing with a fitted polynomial. The noise without aperture stop is approximately peak to peak whereas the residual spectral structures with A and D owing to changing illumination were reduced to peak to peak ,1. Thus an improvement of a factor of 2 3 above the diffuser setup and of a factor of above the naive PDA approach was obtained. We used these results to build a quartz-fiber mode mixer 1112 APPLIED OPTICS Vol. 36, No February 1997

9 Table 2. Peak-to-peak Residual Structures for Various Optical Measures to Reduce the Variation in the Angular Intensity Distribution during Atmospheric Measurements Measure Peak-to-Peak Residual Without Diffuser Diffuser Diffuser Mode mixer Fig. 8. Noise and residual spectral structure of a system, including a mode mixer Figs. 5 and 7. The structures S A S 0 and S D S 0 are smaller by a factor of more than 10 compared with the results without a mode mixer Fig. 2. with a 2-m-long fiber based on the design illustrated in Fig. 7, which was included in our field experiment. 4. Atmospheric Experiments Figure 9 shows the setup of our new long-path DOAS instrument to measure tropospheric trace gases. The instrument employs the coaxial telescope arrangement now widely used. 5,6,13 Light of a xenon arc lamp is collimated with a Newtonian telescope and sent through the atmosphere. After several kilometers the light is reflected by a quartz prism retroreflector array. The reflected light is then received by a second Newtonian telescope inside the Fig. 9. Setup of a long-path DOAS instrument. A combined sending receiving Newtonian telescope of 1.5-m focal length collimates light of a xenon arc lamp and focuses the light reflected by the retroreflectors to the entrance of the mode mixer. The end of the mode-mixer fiber is used as the entrance slit for the spectrograph. Lamp, telescope, and spectrograph detector system are mounted on a frame that is fixed to a table with a universal joint. The frame can be rotated in all directions with the help of two stepper motors. first telescope. We used the outer ring of the main mirror of this combined sending receiving telescope for sending light and the inner part for receiving the light. The central part of the main mirror is shadowed by the smaller secondary mirrors. The light is focused on the quartz fiber of the mode mixer and fed into the spectrograph. The detector and spectrograph are identical to the ones used in the laboratory measurements described above. The telescope together with the lamp and the spectrograph are mounted on a frame, which can be rotated in all directions. The frame can be moved with two stepper motors to adjust the instrument to maximum received intensity. This procedure can be performed automatically to correct a movement of the focus that is due to temperature changes in the atmosphere. To reduce the higher spatial wavelength of the étalon structures in the UV, we changed the PDA to a model with a thinner 1- m protective layer. Measurements showed that the effects of residual structures found in the laboratory could also be reproduced with this PDA. To record spectra of the lamp and the diode array sensitivity, a small shortcut mirror together with a lens can be moved into the outgoing collimated light beam by a stepper motor. This mirror is rotated 45 with respect to the telescope axis and reflects the outgoing light toward the fiber. The lens can then be used to focus the collimated beam on the fiber, producing a shortcut in the light path see Fig. 9. We tested the instrument in Heidelberg with a total light path of 7.5 km and the same wavelength region as in the laboratory measurements. Table 2 lists the peak-to-peak residuals of the different measures to correct nonuniform illumination of the spectrograph. The size of the encountered residuals is only a factor of 1.5 higher than the residuals derived in the laboratory Table 1. Figure 10 shows a typical example of an atmospheric spectrum at 300 nm of a DOAS measurement of O 3,NO 2,SO 2, and HCHO. The top spectrum is the measured spectrum after electronic offset and atmospheric background light have been corrected. The spectrum was divided by a lamp spectrum measured with the shortcut mirror in the light path to correct the diode response and lamp structures: The figure shows the logarithm of these spectra. We evaluated the atmospheric spectrum by fitting a linear combination of the pure trace gas absorptions measured in the laboratory. Figure 10 shows the trace gas absorptions scaled by the fit and the resid- 20 February 1997 Vol. 36, No. 6 APPLIED OPTICS 1113

10 Fig. 10. Sample evaluation of an atmospheric DOAS spectrum. To the atmospheric spectrum top trace the absorption spectra of the pure trace gases are fitted. The absorption spectra of O 3,NO 2, SO 2, and HCHO scaled by the analysis routine are shown below. After all the trace gas absorptions are removed, residual structures of peak to peak remain. ual of this analysis. After the removal of the absorption structures from the atmospheric spectrum, there remain residuals of approximately peak to peak that cannot be explained by trace gas absorptions. The size of these residuals is comparable with the residuals found in the laboratory experiments. 5. Conclusion The angular dependence of the PDA response can in principle be explained by dust on the PDA, an irregular protective-layer thickness, and possible irregularities in the angular sensitivity of the diodes. This dependence produces unwanted residual structures when spectra are recorded with light of varying angular intensity distribution. Because of atmospheric effects in DOAS measurements, variations in the angular intensity distribution are practically unavoidable. Because the structures caused by dust particles are not large enough to explain residual structures of 10 2 in the laboratory experiments, an irregular protective layer appears to be the most likely explanation. An estimate of the effect of irregular sensitivity of the diodes is difficult and could not be performed. The experiments in the laboratory and the open atmosphere showed that the residual structures can easily reach the size of 10 2, thus severely degrading the detection limit of DOAS measurements with the PDA approach without further optical elements. These structures can be reduced considerably by the use of mode mixing in multimode quartz fibers to produce a nearly constant angular intensity distribution. The advantage over other diffusers is a more effective mixing and a low intensity loss of 20% in the mode mixer. The parameters derived in laboratory experiments were used to build a quartz-fiber mode mixer for a DOAS field experiment. The technique described here can also be used with other fibers. Experiments in our laboratory, not reported here, showed mode mixing for fiber diameters of as large as 0.8 mm. A variation of the aluminum profile shown in Fig. 5, especially in the height and the distance of the steps, might be necessary to optimize the mode mixer for specific fibers. The experiment shown in Fig. 5 can be used to test the mode mixing and to adjust the pressure on the fiber. The detection of the light with a photodetector is not necessary as the change of intensity distribution in the far field can easily be seen by the eye. To check the effect on the structures caused by the diode array, the use of aperture stops similar to the stops described above is useful and easily accomplished. The exact shape of the aperture stops is not important, as any change of the illumination will give rise to the structures described above. A random movement of the quartz fiber for example, by a turbulent air stream of a fan, averages the different thermal and mechanical states of the fiber and thus makes it less sensitive to any changes in the surrounding environment. We have observed this effect with different fibers and Table 3. Detection Limit of DOAS Long-Path Instruments with SD and PDA detectors a Instrument km O 3 SO 2 NO 2 ppb b ppt c ppt HCHO ppt HONO ppt NO 3 ppt SD PDA PDA PDA a The values for photodiode arrays with light paths longer than 5 km are calculated with the result for the 5 km path. The described instrument has been used with a path length of 12.5 km in Spitzbergen, Norway, yielding approximately the expected detection limits in this table. 6 b ppb, parts per billion c ppt, parts per trillion APPLIED OPTICS Vol. 36, No February 1997

11 fiber bundles and use a fan whenever the fiber cannot be stabilized. The mode mixer improved the detection limit of the instruments by a factor of more than 10, thus reaching and surpassing the detection limits of the older DOAS instruments with slotted disk scanners of Platt et al. 12 Because of the multiplex advantage of the PDA the measurement time 5 min to reach this detection limit is much shorter than with the older systems. In addition the high light sensitivity of the instrument allows the use of longer light paths, thus increasing the detection limit further. Light paths as long as 12.5 km were used to detect background concentrations of atmospheric trace gases. 6 For measurements in the visible spectral range even longer light paths are possible. Table 3 gives the detection limits derived with the new instrument on a 5-km-long light path during the Tropospheric Optical Absorption Spectroscopy project of the European Experiment on the Transport and Transformation of Environmentally Relevant Trace Constituents in the Troposphere over Europe 27 in Weybourne, UK. We used these values to estimate the detection limit for longer light paths. Recent results of the Arctic Tropospheric Ozone Chemistry campaign 6 in Spitsbergen, Norway, in May 1996, in which boundary layer BrO could be detected with a 12.5-km light path, confirmed the performance of our approach. Support by Bundesministeriums für Forschung und Technologie grant 07 EU is gratefully acknowledged. References 1. D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, and A. Volz, OH-radicals in the lower troposphere, Geophys. Res. Lett. 3, D. Perner and U. Platt, Detection of nitrous acid in the atmosphere by differential optical absorption, Geophys. Res. Lett. 6, U. Platt, D. Perner, G. W. Harris, A. M. Winer, and J. N. Pitts, Detection of NO 3 in the polluted troposphere by differential optical absorption, Geophys. Res. Lett. 7, U. Platt, Differential optical absorption spectroscopy DOAS, in Air Monitoring by Spectroscopic Techniques, M. W. Sigrist, ed., Chemical Analysis Series Wiley, New York, 1994, pp M. Hausmann, and U. Platt, Spectroscopic measurements of bromine oxide and ozone in the high Arctic during polar sunrise experiment 1992, J. Geophys. Res. 99, W. Unold, H. Lorenzen-Schmidt, E. Lehrer, J. Stutz, T. Trost, and U. Platt, Arctic Boundary Layer Halogen Oxides during an Ozone Depletion Event in Ny Alesund, Spitsbergen 78 N, in preparation by staff at Institut für Umweltphysik, University of Heidelberg, Heidelberg, Germany. 7. R. W. Sanders, S. Solomon, M. A. Caroll, and A. L. Schmeltekopf, Ground-Based Measurements of O 3,NO 2, OClO and BrO during the 1987 Antarctic Ozone Depletion Event, in Ozone in the Atmosphere; Proceedings of the Quadrennial Ozone Symposium 1988 R. D. Bojkov and P. Fabian, eds. Deepak Publishing, Hampton, Va., 1989, pp U. Platt and D. Perner, Measurements of atmospheric trace gases by long path differential UV visible absorption spectroscopy, in Optical and Laser Remote Sensing, D. K. Killinger and A. Mooradien, eds. Springer, New York, 1984, vol. 39, pp J. M. C. Plane and C-F. Nien, Differential Optical Absorption Spectrometer for Measuring Atmospheric Trace Gases, Rev. Sci. Instrum. 63, J. Stutz and U. Platt, Numerical analysis of DOAS spectra with linear and nonlinear least squares fits, Proceedings of EUROTRAC Symposium 94, P. M. Borell et al. eds. 1994, p.p J. Stutz and U. Platt, Numerical analysis and estimation of the statistical error of differential optical absorption spectroscopy measurements with least-squares methods, Appl. Opt. 35, U. Platt and D. Perner, Ein Instrument zur spektroskopischen Spurenstoffmessung in der Atmosphäre, Fresenius Z. Anal. Chem. 317, H. Axelson, B. Galle, K. Gustavsson, P. Ragnarsson, and M. Rudin, A transmitting receiving telescope for DOASmeasurements using retroreflector technique, in Optical Remote Sensing of The Atmosphere, Vol. 4 of 1990 OSA Technical Digest Series Optical Society of America, Washington, D.C., 1990, pp P. V. Johnston and R. L. McKenzie, Long-Path Absorption Measurements of Tropospheric NO 2 in Rural New Zealand, Geophys. Res. Lett. 11, J. Stutz and U. Platt, Problems in using diode arrays for open path DOAS measurements of atmospheric species, in Optical Methods in Atmospheric Chemistry, H. I. Schiff and U. Platt, eds., Proc. SPIE 1715, P. Knoll, R. Singer, and W. Kiefer, Improving spectroscopic techniques by a scanning multichannel technique, Appl. Spectrosc. 44, T. Brauers, M. Hausmann, U. Brandenburger, and H.-P. Dorn, Improvement of Differential Optical Absorption Spectroscopy using Multi-Channel-Scanning-Technique, Appl. Opt. 21, RL1024SR Data Sheet, EG&G Reticon, Sunnyvale, Calif G. Mount, R. Sanders, and J. Brault, Interference effects in reticon photodiode array detectors, Appl. Opt. 31, J. Stutz, Messung der Konzentration troposphärischer Spurenstoffe mittels Differentieller Optischer Absorptionsspektroskopie: Eine neue Generation von Geräten und Algorithmen, Ph.D. dissertation University Heidelberg, Heidelberg, Germany, T. Gomer, T. Brauers, F. Heintz, J. Stutz, and U. Platt, MFC User Manual, Version 1.98, University Heidelberg, Heidelberg, Germany, J. Reader, Optimizing Czerny Turner spectrographs: a comparison between analytic theory and ray tracing, J. Opt. Soc. Am. 59, D. Perner, MPI Luftchemie, Mainz, Germany personal communication, H. P. Dorn, U. Brandenburger, T. Brauers, and M. Hausmann, A new in-situ long path absorption instrument for the measurements of tropospheric OH radicals, J. Atmos. Sci. 52, D. Marcuse, Coupled Mode Theory of Round Optical Fibers, Bell Syst. Tech. J. 52, M. Imai and T. Asakura, Evaluation of the mode scrambler characteristics in terms of speckle contrast, Opt. Commun. 30, J. Bösenberg, D. Brassington, and P. C. Simon, Instrument Development for Atmospheric Research and Monitoring, European Union publication to be published. 20 February 1997 Vol. 36, No. 6 APPLIED OPTICS 1115