Ruth A. Dyer

A Fast Spectrum-Recovery Method for Hadamard Transform Spectrometers Having Nonideal Masks

A computationally inexpensive method is presented for the recovery of spectra from measurements obtained with Hadamard transform spectrometers having nonideal masks. Normally, N measurements are required in order to recover an N-point spectrum; this method requires N + N0 measurements to be taken, where, typically, N0 ≤ 10. Once the additional measurements have been taken, only O(N[log2N + 2]) arithmetic operations—mostly additions or subtractions—are needed in order to recover the spectrum; a conventional procedure requires O(2N2) operations. Preliminary work for this method is minimal, requiring O(N) operations as opposed to O(N3) for a conventional procedure; this work needs to be done only once for a given spectrometer. The spectrum-estimate obtained is unbiased.

An Efficient Method for Recovering the Optimal Unbiased Linear Spectrum-Estimate from Hadamard Transform Spectrometers Having Nonideal Masks

A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks. This method has the following advantages over other spectrum-recovery techniques: it is computationally efficient, it requires no additional measurements, and it computes an optimal spectrum-estimate. In the method presented, after the mask of the HT spectrometer has been characterized, approximately 3N preliminary arithmetic operations are performed once for a given spectrometer, where N is both the number of spectral resolution-elements desired and the number of measurements required. Each spectrum-estimate to be recovered then requires only an additional O[N(log2N + 4)] arithmetic operations. In contrast, conventional methods for obtaining an optimal unbiased linear spectrum-estimate require O(N3) preliminary operations, and O(2N2) operations during each spectrum-recovery.

Implementation problems in Hadamard transform spectrometry

The multiplex advantage offered by Hadamard transform spectrometry (HTS) can improve the signal-to-noise ratio (SNR) at the output of a spectrometer. However, additional processing of the spectrometer output is required to recover the individual spectral components. A block diagram description of HTS and the spectrum-recovery process is presented. A computer simulation of this model has been developed and can be used to examine the effects of certain nonidealities that may typically be encountered. Traditionally, the inverse Hadamard transform (IHT) has been used as the spectrum-recovery method, but the IHT does not take into account the nonidealities associated with the multiplexing process. Two spectrum-recovery methods that address the problems of nonidealities are presented. The relative performance of all three methods is compared with regard to mean square error (MSE) and the computational efficiency of the algorithms necessary to implement the schemes. An example application is described, and the performance of the three spectrum-recovery schemes is discussed. >

On the Mean-Square Error of Various Spectrum-Recovery Techniques in Hadamard Transform Spectrometry

The multiplexing inherent in the Hadamard transform (HT) spectrometer can result in an improved spectrum-estimate when the detector is the major source of noise. A spectrum-estimate may be further improved by taking into account any nonidealities in the system. In this paper, observations concerning the errors associated with such estimates are presented, with the use of results obtained from computer simulations. Three spectrum-recovery techniques for an HT spectrometer having a nonideal electro-optic mask are considered in terms of the mean-square error (MSE) associated with a given estimate. The discussion of the MSE is with respect to the input spectrum to be estimated, the detector noise, the transmittances of the nonideal mask, and the use of coaddition. Included is a review of the computational efficiency and the statistical bias of each method. The relative performances of the spectrum-recovery methods are presented with examples to help identify the sources of error for each of the techniques.

An introduction to Hadamard spectrometry and the multiplex advantage

The authors consider a special class of problems in which the dominant noise source in the spectrum measurements is the noise generated in the detector itself. In this case, the signal-to-noise ratio of the spectrum estimates can be improved by a multiplexing technique known as Hadamard spectrometry. Specifically, if the MSE (mean-square error) of a single-slit spectrometer is sigma /sup 2/, the MSE of a Hadamard system will be approximately 4/ sigma /sup 2//N. In this expression, N is the number of spectral components to be estimated and the number of measurements to be taken.<<ETX>>

A model for incorporating the effects of nonzero switching-time constants in electrooptic masks used in Hadamard-transform spectrometry

Hadamard-transform (HT) spectrometers offer a multiplex advantage over conventional monochromators, making them very useful in situations in which the signal-to-noise ratio is low. HT spectrometers having no moving parts can be implemented by substituting; an electrooptic mask for the moving mask in the optical path. However, the physical properties of an electrooptic mask introduce two types of nonidealities-static and dynamic-into the measurement system. These nonidealities can cause distortions in the acquired spectra if their effects are neglected in the signal-recovery process. We have developed two complete system models which incorporate the effects of both static and dynamic nonidealities. In addition, we have devised recovery schemes applicable for each system model and have designed computationally efficient implementations of the recovery schemes.<<ETX>>

Development and implementation of a general-purpose Hadamard-Transform spectrometer simulation program

A general-purpose Hadamard-transform spectrometer simulation program has been developed. It combines software that simulates the operation of an HT spectrometer with computationally efficient algorithms for performing recovery of spectre. The incident spectrum fan be encoded with a right-cyclic, left-cyclic or noncyclic encodement scheme. A block-diagram approach is utilized, with blocks allocated for the description of the spectrometer model, the addition of detector noise, and the spectrum-recovery method. The user can choose among various spectometer models and spectrum-recovery schemes which have been previously developed. A source file is used to specify the blocks to be included, the input and output variables of each block, the mask size, the values of various other constants used by the program, and any changes to be made if additional models or recovery methods are to be used in subsequent runs. Various algorithms are made available to implement the right-cyclic matrix inversions, circular correlations and vector-matrix multiplications required. In the computation of the spectrometer output and the spectrum-estimate. This paper presents important features of the simulation program and shows an example source file.

Implementation problems in Hadamard spectrometry

The multiplexing offered by Hadamard-transform spectrometry can improve the signal-to-noise ratio at the output of a spectrometer. Traditionally, the inverse Hadamard transform (IHT) has been used to recover the individual spectral components, but the IHT does not take into account the nonidealities associated with the multiplexing process. A system model has been developed which addresses nonidealities in the multiplexer, noise introduced at the detector, and choice of method for spectrum recovery. A computer simulation of the model has been developed and can be used to examine the effect of certain nonidealities that may typically be encountered. Three different spectrum-recovery schemes are examined, and their relative performance is compared with regard to mean-square error and to the computational efficiency of the algorithms necessary to implement them. An example application is described, and the performance of the three spectrum-recovery schemes is discussed.<<ETX>>

Right-cyclic Hadamard coding schemes and fast Fourier transforms for use in computing spectrum estimates in Hadamard-transform spectrometry

Two computationally efficient spectrum-recovery schemes have been developed for use by Hadamard-transform spectrometers that have static and dynamic nonidealities in their encoding masks. When a right-cyclic Hadamard pattern is used to encode the mask, a fast Fourier transform (FFT) algorithm or a Trench algorithm can be used to obtain one of the matrix inverses, and an FFT can be used to compute the vector-matrix product, both of which are required in the spectrum-recovery process. In general, the number of mask elements is not an integer power of two, normally requiring that non-radix-2 FFT algorithms be used. However, with appropriate zero-padding of the vectors, radix-2 FFTs can be used to compute the required vector-matrix product. Various combinations of algorithms were used and the total computation times were compared in order to determine the most efficient means of computing the spectrum-estimate. The results indicate that the number of elements in the mask is an important factor in determining which combination of algorithms provides the most efficient recovery of the spectrum-estimate.<<ETX>>

Informal Discussion and Reception - Women in Engineering

There is a resurgence in space exploration activity. In 2004, the US announced plans to return to the moon by 2020. Supporting this new mission requires a new generation of launch and exploration vehicles. Recently, Chinas space program has placed astronauts into orbit and is planning crewed lunar exploration missions by the end of the next decade. The remarkable photographs returned by the Mars rovers and the longevity of the rovers have underscored the promise of autonomous exploration vehicles. Rutans company, Scaled Composites, won the X Prize in 2004; we may be on the brink of a new wave of commercial and tourist access to space. Panelists will provide brief position statements amplifying the unique aspects of their work as they relate to significant challenges of measurements in support of space exploration. The discussion led by the panel will explore the ramifications for the measurement community. During the remaining portion of the session, panelists and session attendees will discuss mechanisms for furthering technical interchange at future conferences and workshops. Informal Discussion and Reception Women in Engineering This event scheduled for May 1, 2007, 3:30-5:30PM (room Sawa) will be facilitated by Ruth A. Dyer (Kansas State University, USA). It will provide an informal networking opportunity for women scientists and engineers in academe, industry, and government. Anyone interested in promoting greater involvement of women in the l&M Society also will be welcome. Members of the Instrumentation and Measurement (I&M) Society Administrative Committee will attend and participate in the discussion. Attendees will have the opportunity to meet new colleagues, as well as share ideas and strategies with one another regarding career advancement. Topics that will be addressed include opportunities for greater involvement in the l&M Society; similarities and differences in the university and other workplaces in various countries and what we can learn from one anothers experiences; importance of mentoring and cultivating a circle of mentors; and suggestions from the participants as to how the l&M Administrative Committee can engage more women members and use their talents to enhance the l&M Society.