APPLIED SPECTROSCOPY 1303

8. J. D. Frantz, J. Dubessy, and B. Mysen, Chem. Geol. 106, 9 (1993).9. D. A. Palmer, G. M. Begun, and F. H. Ward, Rev. Sci. Instrum. 64,

1994 (1993).10. Y. E. Gorbaty and G. V. Bondarenko, Rev. Sci. Instrum. 66, 4347

(1995).11. Y. Ikushima, K. Hatakeda, N. Saito, and M. Arai, J. Chem. Phys.

108, 5855 (1998).12. W. S. Hurst, M. S. Hodes, W. J. Bowers, V. E. Bean, J. E. Maslar,

P. Grif� th, and K. A. Smith, J. Supercrit. Fluids 22, 157 (2002).13. Y. E. Gorbaty and G. V. Bondarenko, Appl. Spectrosc. 53, 908

(1999).14. Y. E. Gorbaty, E. Venardou, E. Garcia-Verdugo, and M. Poliakoff,

Rev. Sci. Instrum. 74, 3073 (2003).15. P. A. Hamley, T. Ilkenhans, J. M. Webster, E. Garcia-Verdugo, E.

Venardou, M. J. Clarke, R. Auerbach, W. B. Thomas, K. Whiston,and M. Poliakoff, Green Chem. 4, 235 (2002).

16. A. R. Katritzky, M. Balasubramanian, and M. Siskin, Energy Fuels4, 499 (1990).

17. D. Lien-Vien, N. B. Colthup, W. G. Fateley, and J. G. Grasseli, TheHandbook of Infrared and Raman Characteristic Frequencies ofOrganic Molecules (Academic Press, San Diego, 1991).

18. S. W. Joo, S. W. Han, H. S. Han, and K. Kim, J. Raman. Spectrosc.31, 145 (2000).

19. J. B. Dunn, M. L. Burns, S. E. Hunter, and P. E. Savage, J. Super-crit. Fluids, paper in press (2003).

20. S. Yin and T. Sato, Ind. Eng. Chem. Res. 39, 4526 (2000).21. S. J. Barlow, G. V. Bondarenko, Y. E. Gorbaty, T. Yamaguchi, and

M. Poliakoff, J. Phys. Chem. A 106, 10452 (2002).

Single Scan Cosmic Spike RemovalUsing the Upper Bound SpectrumMethod

DONGMAO ZHANG, JEANETTE D.HANNA, and DOR BEN-AMOTZ*Department of Chemistry, Purdue University, West La-fayette, Indiana 47907-1393

Index Headings: Cosmic spike; Charge-coupled device; CCD; Sur-face-enhanced Raman spectroscopy; SERS; Raman; Upper boundspectrum; UBS.

Two previous papers have reported the removal of cos-mic spikes from charge-coupled-device (CCD) spectraand images using variants of the upper bound spectrum(UBS) method.1,2 These previous UBS implementationsrequire either comparison of data derived from two ormore CCD scans,1 or analysis of a large data set com-prising many spectra.2 However, in many applications,particularly those involving chemically reacting and/orphotosensitive systems, it would be desirable to avoid theneed to multiply read-out the CCD. This work demon-strates a new variant of the UBS method in which datapoints from different pixels in a single CCD scan are usedto generate comparison spectra for spike identi� cationand removal.

This method is applicable to situations in which several

Received 3 March 2003; accepted 27 May 2003.* Author to whom correspondence should be sent.

rows of CCD pixels contain spectral data derived fromthe same sample. The required UBS comparison spectraare obtained by grouping spectra derived from spatiallyseparated CCD rows (referred to as row spectra) to createtwo or more composite spectra for UBS comparison, asdescribed below. The optimal number of comparisonspectra needed to effectively implement the UBS methoddepends on the average number of spikes in each CCDscan, as described previously.1 Implementation of thisspike removal method is demonstrated using both con-ventional and surface-enhanced Raman (SERS) spectraobtained using two different types of dispersive Ramaninstruments.

A pre-condition for implementing the original UBSmethod 1 is that the Raman spectral features in the com-parison spectra have the same shape (although not nec-essarily the same overall intensity). However, spectrafrom different CCD rows may be somewhat different inshape as a result of imperfections in the spectrometercollection/diffraction optics, which leads to non-unifor-mity in the spectrometer throughput for signals going todifferent regions of the CCD detector surface. Such dif-ferences can be minimized by grouping alternate CCDrow spectra into different comparison spectra, so eachcomparison spectrum represents the sum of non-neigh-boring row spectra. More speci� cally, the following is anoutline of the procedure we have used to generate suit-able UBS comparison spectra.

(1) De� ne the region of interest (ROI) on the CCD.Record the signal intensity in the ROI as a datamatrix D(m, n), where n corresponds to the numberof pixels in the wavelength (horizontal) axis, andm is the total number of row spectra (vertical pix-els) contained in D .

(2) Determine C, the required number of UBS com-parison spectra according to the estimated densityof cosmic spikes (required in order to reduce thechance that all the successive spectra have spikesin the same position), as described previously.1

(3) Split the m row spectra in D into C groups byalternately selecting row spectra such that rowspectrum i belongs to group k if modulo (i 2 1,C ) 5 k 2 1, where k 5 (1 . . . C ) and i 5 (1 . . .m). The C comparison spectra are obtained bysummation of the spectra in each group.

(4) Apply the UBS method to the C comparison spec-tra in order to identify and remove suspected spikeartifacts.1 The UBS method uses multiple spectrato statistically distinguish spectral features fromcosmic spike events. The summation of the result-ing spike-free comparison spectra is the UBS out-put spectrum.

Two Raman instruments were used to collect spectrafor testing the UBS method. One is a lens-coupled single-point micro-Raman instrument3 used to acquire SERSspectra of a 1023 M adenine solution deposited on Agcolloid nano-particles immobilized on a glass slide.4 Theother is a � ber-bundle coupled portable Raman imagingsystem, similar in design to a Near-IR Raman ImagingMicroscope,5 used to collect Raman spectra from a phar-maceutical Tylenol tablet. In both cases single pixel bin-ning (1 3 1) was used to read-out the CCD signal in

1304 Volume 57, Number 10, 2003

FIG. 1. Spike removal from the SERS spectrum of adenine. (A) CCDspectral image in gray scale, with circled dark spots indicating the lo-cation of high intensity cosmic spikes. (B) Raw spectrum resulting fromthe summation of the pixel intensities in each image column. (C ) UBSprocessed spike-free output spectrum. (D ) UBS difference spectrumshowing spikes that have been identi� ed and removed from B.

FIG. 2. Spike removal from the Raman spectrum of Tylenol. (A) CCDimage showing sharp spikes (dark spots) and Raman bands (verticalbands). (B) Raw spectrum from one of the input comparison spectra.(C ) The same spectrum after UBS spike removal. (D ) Difference spec-trum showing the spikes removed from B.

order to facilitate the creation of comparison spectra fromalternate row spectra (as described above).

The SERS spectra were obtained using 0.1 mW HeNeexcitation laser light focused to a 7 mm diameter spot onthe sample surface and a CCD integration time of 100 s.3

The astigmatic spectrograph (ISA 320) used to collect theRaman signal spreads each wavelength of a circular lightsource at the entrance slit to a vertical band about 90rows tall and 4 pixels wide at the CCD plane (PrincetonInstruments LN/00D-1152E).

The Tylenol Raman spectra were obtained using a 1mW HeNe excitation laser and intentionally misalignedcollection optics so as not to saturate the CCD over a300 s integration time. The Raman signal was collectedwith a 37-� ber bundle (each with a 50 mm core diameter),arranged in a close-packed circular array at the collection(sample) end and a linear stack at the detection end,which served as the spectrograph (Acton SpectraPro 300)entrance slit. The 2.5-mm-tall detection � ber stack wasimaged onto about 100 rows of CCD pixels (Roper Sci-enti� c RTE/CCD-256-H).

The CCD spectral image of the SERS signal of adenineobtained in 100 s of integration time is shown in Fig. 1A.The intense localized cosmic spikes (circled points) aremuch stronger than the weaker Raman signal, which isprimarily evident as a vertical band at around horizontalpixel number 272 (which corresponds to the aromatic Ra-man shift band at 720 cm21). Figure 1B shows the sum-mation spectra of all 90 rows. The six prominent spikes

that are evident in Fig. 1B derive from the circled spotsin the CCD image (Fig. 1A). In order to ensure that nocosmic spikes appear in the same position in every spec-trum, four comparison spectra (not shown) were gener-ated from the 90 row spectra and processed with the UBSmethod. The summation of all four of the comparisonspectra, after UBS spike removal, is shown in Fig. 1C.Figure 1D shows the difference between the spectra inFigs. 1B and 1C, and thus contains all the spikes thatwere identi� ed and removed from the input spectrum(Fig. 1B).

Figure 2A shows the CCD spectral image of Tylenolobtained with an integration time of 300 s. The high den-sity of spikes (dark points in Fig. 2A) required the useof six comparison spectra generated from 101 input CCDrow spectra.1 Figures 1B and 1C show one of the sixcomparison spectra before and after UBS processing,while Fig. 1D shows the resulting difference spectrumcontaining all the spikes that were identi� ed and re-moved. Similar results were obtained from the other � vecomparison spectra.

In summary, the above results demonstrate that theUBS spike removal algorithm may be effectively imple-mented by generating comparison spectra generated byinterleaving row spectra from a single CCD scan. Bothvery large spikes and spikes that are smaller in peak in-tensity than the Raman bands have been effectively iden-ti� ed and removed without introducing any apparent dis-tortion of underlying Raman spectral features. The small-

APPLIED SPECTROSCOPY 1305

est spikes that may be removed using the UBS methodare determined by the noise in the spectrum.1 The onlyprerequisites to effective spike removal are (1) that thesame spike does not contaminate all comparison spectraand (2) that all comparison spectra contain (Raman) fea-tures of the same shape (but not necessarily the sameoverall intensity); no other restriction is placed on spikeheight, width, or position. The effectiveness of the UBSmethod is not degraded by spike blooming or overlapwith spectral feature. No distortion of spectral features isproduced by UBS removal, even in spectral features ofcomparable width to spikes.1

ACKNOWLEDGMENTS

This work was supported by the Of� ce of Naval Research. The au-thors would also like to thank Yong Xie and Corasi Ortiz for providingthe SERS substrate and the adenine sample used in this work.

1. D. Zhang, K. N. Jallad, and D. Ben-Amotz, Appl. Spectrosc. 55,1523 (2001).

2. D. Zhang and D. Ben-Amotz, Appl. Spectrosc. 56, 91 (2002).3. F. LaPlant and D. Ben-Amotz, Rev. Sci. Instrum. 66, 3537 (1995).4. R. G. Freeman, K. C. Grabar, K. J. Allison, R. M. Bright, J. A.

Davis, A. P. Guthrie, M. B. Hommer, M. A. Jackson, P. C. Smith,D. G. Walter, and M. J. Natan, Science (Washington, D.C.) 267, 1629(1995).

5. B. L. McClain, H. G. Hedderich, A. D. Gift, D. Zhang, K. N. Jallad,K. S. Haber, J. Ma, and D. Ben-Amotz, Spectroscopy 15, 28 (2000).

Virtual Column Method forCorrecting Masking Effects inHadamard Transform Systems

QUENTIN S. HANLEYDepartment of Biological and Chemical Sciences, Uni-versity of the West Indies Cave Hill Campus, St. Mi-chael, Barbados

Index Headings: Hadamard transforms; S matrices; Hadamardtransform spectroscopy.

INTRODUCTION

Prior studies have noted a variety of mask-related ef-fects in Hadamard transform systems. This note presentsa strategy for correction of several types of � rst-order,second-order, and spreading-related effects. The methodis applicable to cases in which adjacent mask elementsin� uence the ability of an element to provide ideal ‘‘on’’or ‘‘off ’’ behavior. Examples of such errors include: un-der- and over-cutting errors, temporal errors in liquidcrystal displays (LCDs), and diffraction-limited maskspreading. In previous studies of these types of errors,uniform � elds and smooth spectroscopic features couldnot be properly corrected without recourse to an external

Received 24 September 2002; accepted 2 June 2003.E-mail: qhanley@uwichill.edu.bb.

calibration procedure. The strategy given here is to in-tentionally truncate the rows of the design matrix or setselected columns in the matrix to zero and use the mod-i� ed matrix to generate the encoding mask. This resultsin ‘‘virtual’’ pixels whose values are known to be zero.By applying a minimization procedure using these pixels,models of mask behavior can be � t and the errors sub-sequently corrected. In previous work, echoes were cor-rected using a calibration procedure based on knownsamples. Using simulations of mask behavior, the pro-cedure described was shown to work for cases of maskerrors arising from the in� uence of neighboring pixels,including cases where all of the non-virtual pixels containuseful information. Here, several types of mask errors areconsidered, a strategy for recovering the characteristicsof the error is demonstrated, and corrections are applied.The investigation of the virtual column procedure foundpreviously undescribed mask effects, which have beennamed discontinuity errors.

Hadamard methods continue to be of interest in chem-istry,1,2 optics,3 and spectroscopy.4–8 Recently, several pa-pers have been published on the behavior of non-idealmasks or ideal masks used under non-ideal condi-tions.7,9,10 While the theory of mask effects has been treat-ed quite extensively, a more limited literature exists doc-umenting artifact-correcting procedures.11–14 One problemof particular interest arises from a class of Hadamard sys-tems that may exhibit echo artifacts even in the absenceof errors in the mask itself.9,10 The appearance of theseartifacts depends on the length of the sequence, and in-formation about the artifact-inducing phenomena can beinferred from the artifact behavior. Further, in caseswhere no mask defect is present, under some conditionsthe effect can vary as experimental conditions change.These types of errors are addressed in this note. The rel-evant literature should be consulted for other types ofmasking effects.11–17

An example of such a system was noted in the behav-ior of a confocal Hadamard transform spectroscopy sys-tem.10 This system exhibited echoes due to diffraction-limited optical spreading in the presentation of the maskto a sample followed by detection through the samemask. The echoes observed in this system were mitigatedby the use of a calibration procedure. The calibrationspecimen consisted of a sparsely populated � eld of � uo-rescent beads. This bead specimen contained large areasof recognizable background between beads, which couldbe used to identify the position of echoes. These back-ground regions were used to perform a subsequent min-imization procedure. Although successful, there are sev-eral disadvantages to this approach. (1) It requires askilled operator to identify regions suitable for minimi-zation. (2) It would be dif� cult to implement in a Had-amard transform system using sequences of length otherthan 2 n 2 1. (3) It must be repeated each time a modi-� cation is made to the system. (4) The calibration maynot robustly transfer from the calibration specimen to thesample under observation. Any increases in aberrationssuch as those that would result from changing the depthof observation in a sample might decrease the validity ofthe calibration procedure. Similar dif� culties would beobserved when the bandwidth of a wavelength-encodinginstrument is changed. (5) It does not generalize to mask