The focus of this study is to find the appropriateness of the Levenberg–Marquardt (LM) neural network (NN) training algorithm for recognition of odor patterns associated with an electronic nose (e-nose). Multiple time-patterns represent step response of the array of sensors to the odorants. The experiments are performed on four representative classes of odorants: coffees, fragrances, hog farm air, and cola beverages. The odor recognition system is composed of a Karhunen–Loeve (KL) based pre-processing unit, and a feedforward neural network with the LM training algorithm. The parameters of the pre-processing unit and the neural network are fine-tuned using a genetic algorithm. Back-propagation algorithm with adaptive learning rate is selected as a standard neural network training method, for the purpose of comparison. The results of the experiments indicate that the LM algorithm provides high correct recognition ratios. In addition, the results confirm that the LM method outperforms the back-propagation (BP) method with adaptive learning rate, for the classes of the odorants provided in this study.

Performance of the Levenberg–Marquardt neural network training method in electronic nose applications

Sensitivity, repeatability, and discernment are three major issues in any classification problem. In this study, an electronic nose with an array of 32 sensors was used to classify a range of odorous substances. The collective time response of the sensor array was first partitioned into four time segments, using four smooth time windowing functions. The dimension of the data associated with each time segment as then reduced by applying the Karhunen-Loeve (truncated) expansion (KLE). An ensemble of the reduced data patterns was then used to train a neural network (NN) using the Levenberg-Marquardt (LM) learning method. A genetic algorithm (GA)-based evolutionary computation method was used to devise the appropriate NN training parameters, as well as the effective database partitions/features. Finally, it was shown that a GA supervised NN system (GANN) outperforms the NN-only classifier, for the classes of the odorants investigated in this study (fragrances, hog farm air, and soft beverages).

Using neural networks and genetic algorithms to enhance performance in an electronic nose

The imaging characteristics of a perfect lens partially masked by a linear polarizer can be varied continuously either by rotating an analyzer placed at the output side or by changing the state of polarization of the input beam. In this paper we study the frequency-response characteristics and the point-spread function of such a system. It is also shown that the proposed system can be adapted either for apodization or for superresolution simply by rotating the analyzer. The fact that the unpredictable phase introduced by the mask has no harmful effect on the performance of the system makes it convenient for several applications. Expressions are obtained for the optical transfer function and the point-spread function of such a system. Some specific cases are illustrated graphically, and some probable applications are discussed.

Frequency-response characteristics of a perfect lens masked by polarizing devices

It is well known that circular symmetric phase and amplitude coatings on the lens aperture modify the imaging qualities of a lens. The present paper shows that the effects of such phase and amplitude coatings on the imaging properties of a lens can be achieved by using suitably oriented polarization masks on the lens aperture. The fact that the response of such a system can be continuously varied by changing the orientation of the polarizing devices included in the system lends it a versatility unobtainable by the use of conventional phase and amplitude coatings on the lens aperture.

Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks

A nonlinear quantitative structure anti-HIV activity relationship study was presented for modelling and predicting pyrryl aryl sulfones cytotoxicity data. Levenberg-Marquardt artificial neural network was used to link molecular structures and cytotoxicity data. A data set consisting of 27 derivatives of 1-[5-chlorophenyl) sulfonyl]-1H-pyrrole was used in this study. Among a large number of calculated descriptors, only eight significant molecular descriptors were obtained by stepwise regression, as the most feasible descriptors, and then they were used as inputs for neural network. The data set was randomly divided into 20 training and 7 validation sets and the neural network architecture and its parameters were optimized. The prediction ability of the model was evaluated using the validation data set, leave-one-out cross-validation and response randomization method. The mean square errors and mean absolute errors for the validation data set were 0.0067 and 0.066, respectively, and for the leave-one-out method, they were 0.013 and 0.087, respectively. The results obtained showed the excellent prediction ability and stability of the proposed model in the prediction of cytotoxicity data of the corresponding anti-HIV analogues.

Modelling of cytotoxicity data (CC50) of anti-HIV 1-[5-chlorophenyl) sulfonyl]-1H-pyrrole derivatives using calculated molecular descriptors and Levenberg-Marquardt artificial neural network.

The optical frequency response of a perfect lens partially masked by a retarder has been studied. The optical transfer function (OTF) of such a system depends upon the relative orientation of the analyser, placed at the output, relative to the slow and fast axes of the mask, and also on the relative aportioning of the lens aperture by the mask. The OTF of the system also depends upon the retardation introduced by the mask. In the present paper, we have computed the OTF of the masked lens for different values of the relevant parameters with and without the analyser at the output.

Frequency Response Characteristics of a Perfect Lens Partially Masked by a Retarder

The Levenberg-Marquardt version of least squares, namely the damped least-squares method, is widely used in lens design optimization. Several modifications of the approach have been proposed to accelerate convergence of the optimization procedure. Recent developments in nonlinear optimization theory indicate that the basic Gauss-Newton method of least squares can play a useful role for this purpose in many practical applications. Giving a brief outline of the pertinent developments, the paper reports on the feasibility of using the basic Gauss-Newton method of least squares in practical lens design optimization when, at each iteration, a line search procedure follows the least-squares solution to determine the optimum change vector for that particular iteration stage. It is observed that incorporation of the line search procedure provides good convergence even without any damping of the least-squares procedure. Some illustrative numerical results are presented.

Role of line search in least-squares optimization of lens design

Birefringent filters can be used for tuning lasers, with some advantages over prisms, gratings and tilted etalons. In this paper the transmission characteristics of a new mixed birefringent filter are investigated. The term ‘mixed’ is used because both circular birefringence and linear birefringence have been utilized in the fabrication of this filter. It has a loss-less core, formed by a cascaded system of alternate rotators and retarders, and a linear polarizer at each end. The performance of this filter is better because of the more effective suppression of side peaks. Unlike previous birefringent filters, this one may be used inside a linear resonator.

A new mixed birefringent filter

Accurate evaluation of aberration derivatives plays a major role in the success of lens design optimization algorithms based on least squares approach. In practice, one often takes recourse to finite difference approximations for evaluating these derivatives. Since the accuracy of such approximations depends upon the aberration and the variable in question, and on the magnitude of the increment applied to the system parameter, the choice of a common optimum increment for all the variables poses a tricky problem. With the backdrop of a statement of the errors associated with approximating derivatives by finite differences, this paper presents the results of our search for a working rule of thumb for the purpose.

Jaya Basu

Papers

Frequency Response Characteristics of a Perfect Lens Partially Masked by a Retarder

Role of line search in least-squares optimization of lens design

A new mixed birefringent filter

Numerical Evaluation of Aberration Derivatives

Optics and Lasers Including Fibers and Optical Waveguides