1. Introduction

Nonlinear optical principles such as two photon absorption, excited state absorption, nonlinear scattering, self focusing etc have potential applications for nonlinear transmission. These nonlinear processes reduce the transmittance significantly for high inputs while offering linear transmittance at low intensities. Chromophores that exhibit nonlinear absorption such as reverse saturable absorption (RSA) and two-photon absorption (TPA) have been well studied for optical power limiting, phase contrast imaging, phase filtering, optoelectronic and photonic devices [1–11]. Reverse saturable absorbing chromophores are among the most promising materials for power limiting applications due to high linear transmittance, a variable and potentially low limiting threshold, fast response and large dynamic range [12, 13]. The limiting threshold can be set either by the concentration of the nonlinear absorbing medium or by the area of the focal spot [14, 15].

On the other hand, the manipulation of spatial frequencies of two dimensional images at the Fourier plane is also well studied for applications in optical information processing [16] such as edge enhancement, character recognition, image correlation and more recently medical image processing [17–21]. An optical lens can map different spatial frequencies to different points in the focal plane – low spatial frequencies at the center and high spatial frequencies on the edge. In conventional technique, a spatial filter is placed at the Fourier plane to block the undesired spatial frequencies of the image. An inverse Fourier transform of the residual beam will display the processed image. However, it is a difficult task to exactly locate the desired spatial frequency band and process it in real time using the conventional techniques since the filter is not all-optically and continually controllable and the images being processed are normally complex. Hence there is a need for a real time filtering technique that can optically locate as well as process the desired spatial frequency bands in applications for information processing and optical computing.

In the literature several Fourier optical image processing techniques are demonstrated using lower power cw lasers [7, 22–25]. Xuan et al exploited optical nonlinearities like two photon absorption and stimulated Raman scattering for real time all optical imaging techniques for contrast improvement and contrast reversal in standard nonlinear liquids like acetone and CS₂ [7]. Castillo et al utilized the Kerr-type nonlinear property of bacteriorhodopsin film for self-induced Zernike-type filter and obtained phase-contrast images [20]. Joseph et al demonstrated a self-adaptive all-optical Fourier image processing system using photo-induced dichroic characteristics of bacteriorhodopsin (bR) film [22]. The filtering technique is based on a mechanism of encoding different spatial frequency components of an input image to different polarization states in bR films using the intensity features of spatial frequency components. The desired components can be selected by an analyzer. Thoma et al used photo-controlled transmission properties of bR films for spatial filtering [23]. Chang et al used two-beam coupling property of photorefractive materials to spatially amplify the desired frequency band of the Fourier spectrum [24]. More recently, Shih et al demonstrated edge-enhancement and image addition-subtraction operations using nonlinear photosensitive dye-doped nematic liquid crystal films [25].

In this paper we demonstrate that a power limiting mechanism can potentially be used for processing and filtering spatial frequencies of any two dimensional image by incorporating a power limiting material at the Fourier plane. In general, the Fourier spectrum of objects possesses low spatial frequencies at high intensities and high spatial frequencies at low intensities except for some special cases like fingerprints. We show that low spatial frequencies are blocked due to their nonlinear absorption in power limiting materials at high intensities while the high spatial frequencies pass through due to linear absorption at low intensities. We also show that continual band-block filtering can be achieved by controlling the incident beam intensity. The continual band-block is possible only for cases where the Fourier spectrum contains monotonous decrease in intensity from zero to high frequencies. As a fringe benefit, when the same experimental setup for both power limiting experiment and optical image processing are used, as in the case of image bearing intense laser beam, the sensitive detectors are potentially protected by blocking the intense low spatial frequencies, while detecting the essential features of the image by detecting the weak high spatial frequencies.

The proposed technique is relatively simple compared to the other image processing techniques that are available in the literature [23–26]. They either use a spatial mask at the filtering plane as in the case of conventional image processing or employ a reference (actinic beam) to perform the image processing or requires cross polarization. While spatial mask is cumbersome and requires precise alignment, the techniques that employ reference beam need to be performed on a vibration isolation table as they involve interference. In contrast, this technique performs the image processing using two lenses and a neutral density filter. Apart from its simplicity, this technique is self-adaptive to the background intensity (amount of dc) of image.

2. Results and discussion

Porphyrins and Phthalocyanines are well known nonlinear absorbing materials because of their strong excited state absorption from both the triplet as well as the singlet states. These molecules were found to have strong reverse saturable absorption and fast response times, the desired criteria for making useful photonic devices. They are proven to be among the most effective optical limiters in the visible region. Reverse saturable absorption (RSA) materials are chosen against two-photon absorption (TPA) because of low limiting thresholds. TPA is dependent on irradiance (Watts/cm²), which means the energy of long pulses should be relatively large before limiting occurs, while excited-state absorption (ESA) is dependent on fluence (Joules/cm²) – initiated by reverse saturable absorption.

Figure 1 illustrates the schematic of the experimental setup. A frequency doubled Continuum Minilite Nd: YAG laser (5 ns pulses at 10 Hz and 25 mJ/pulse, 532 nm wavelength) is used for the study. The beam is spatially filtered and well collimated to uniformly illuminate the object. A 10 cm focal length lens (L₁) is used to obtain the Fourier spectrum of the object. At the Fourier plane, a 2 mm path length cell containing chromophore solution, 0.02 g of 5, 10, 15, 20-tetra (4-pyridyl)-21H, 23H porphine (TpyP) dissolved in 10 ml of chloroform, is placed for real-time processing of spatial frequency information contained in the object. The inverse Fourier transformation of the filtered spectrum is obtained using another 10 cm focal length lens (L₂) and the residual beam is imaged on to the CCD detector placed at the back focal plane of the second lens. Neutral density filter is used to vary the input beam intensity. Part of the inverse Fourier transformed beam is deflected on to the power meter to obtain the power limiting characteristics simultaneously. As the area of the CCD detector and the power meter are about same, full beam area is used in measuring the power.

 

Fig. 1. Schematic of the experimental setup used to observe the edge enhancement using the nanosecond laser. Inlet shows the Fourier spectrum beam profile. NDF: neutral density filter; CL: collimating lens; and Ls: lenses. Sample cell has 2mm path length and contains Porphyrin solution as a nonlinear absorbing medium.

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Initially we performed power-limiting measurements to study the filtering property of our scheme by removing the object in the Fig. 1. As there is no object present, the plane wave is focused (Fourier transformed) by lens L₁ on to the sample cell. The nonlinear transmission characteristic of the TpyP has the profile similar to the one shown in Fig. 2(a). This variation of input intensities can be used to simulate the intensities in different spatial frequency bands of Fourier spectrum of the image. In general the spatial frequency distribution at the Fourier plane can be categorized into different intensity bands – low spatial frequencies at the center with high intensities and high spatial frequencies on the edges with low intensities. Thus the power limiting characteristics can be exploited for filtering property, which is gradually controllable with input intensity. In the case that the input image is carried by a low intensity beam, all the spatial frequencies are transmitted through the sample cell, that is, no processing takes place. As the incident, intensity is increased above the threshold value for power limiting the low frequencies begin to diminish as they occur at high intensities. The limiting for low spatial frequencies can be raised by increasing the incident intensity. This is a significant feature for practical applications in imaging processing and optical computing. The power-limiting curve for a given sample facilitates in the calculation of required input intensities to obtain the desired band of spatial frequencies.

To illustrate the feasibility of image processing, a binary test object “E” is used and the incident intensities are measured after the beam expander and before the collimation. The inlet of the Fig. 1 shows the typical depiction of the Fourier spectrum where low spatial frequencies of the object are focused at the center with high intensity and high spatial frequencies at the edge with low intensities. When the object is placed in the optical path and input intensity is varied from 0 to 1.5 mJ, Fig. 2 shows the power limiting characteristics of the sample as well as the processed images captured at different power limiting points. The power measurements recorded by the power meter reveal the optical limiting characteristics of image processing as shown in Fig. 2(a) while the CCD captured the edge enhancement effects of the object at the corresponding incident beam energies, shown in Fig. 2(b). When the intensities are low, below the limiting threshold, the absorption is in the linear regime and the entire information of the object is transmitted through the sample without any processing as shown in Fig. 2(b) (i). The corresponding position on the power-limiting curve is marked as (i). As the input intensities are varied by changing neutral density filter (NDF), at limiting threshold the low spatial frequency intensities will reach sufficient level to trigger excited state absorption in the sample and begin to diminish as shown in Fig. 2(b) (ii). When input intensity if is increased further, the intensity of low spatial frequency band (including DC) is beyond the power limiting threshold. So in this region of the sample the molecules undergo excited state absorption and thus low spatial frequency band gets absorbed. However, at the same time the intensity of high spatial frequencies striking the sample are well below the power-limiting threshold and thus transmitted without being absorbed as shown in Fig. 2(b) (iii). A near perfect edge enhancement of the object is observed when the input intensities are well above the limiting threshold as depicted in Fig. 2(b) (iv).

 

Fig. 2. (a) Power limiting characteristic display of sample 1. (b) Processed images showing the edge enhancement of the object E. (i) thru (iv) are the points where the processed images are captured using CCD camera.

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The proposed technique is self-adaptive to the low spatial frequency information contained in the object. When the object is changed, the spatial frequency spread at the Fourier plane will change. Since the image processing is dependent on the threshold intensity to block the low spatial frequencies, simply by controlling the incident beam intensity edge-enhancement can be obtained. This is a significant advantage compared to the conventional optical filtering where one has to first properly scale the size of the high pass filter and then position it precisely at the Fourier plane.

A novel feature of the proposed technique is the ease at which continual band-block filtering can be performed for objects that has monotonous decrease in intensity from zero to high frequencies. Such an action using conventional image processing technique is complicated – a series of spatial filters are required and each time precise size and alignment of the filter is demanded. In the present case it can be performed simply by changing the intensity of the beam. Using the transmission curve similar to Fig. 2(a) one can approximate the intensities required for an image to obtain the desired band of spatial frequencies at the output as the input intensity is increased the spatial frequencies starting from low to high frequencies are blocked. The processed images of the grating chart in Fig. 3 demonstrate the applicability. When the input intensity is below the power-limiting threshold, 0.02 mJ, only linear absorption is present and the 4-f configuration will image the object onto the CCD camera without any spatial frequency filtering as shown in Fig. 3(a). As the input intensity is increased above the threshold, 0.05 mJ, some of the low spatial frequencies are blocked resulting in a partial edge-enhancement of the image. Figure 3(b) shows the processed image. The higher limit bar of the spatial frequency blocking is set by the incident beam intensity and can be raised by increasing the intensity. When the input intensity is increased to 0.47 mJ higher spatial frequencies are blocked resulting in the image shown in Fig. 3(c). Upon increasing the input intensity to 0.7 mJ more spatial frequencies are absorbed resulting in near perfect edge-enhancement to the entire exposed area of the grating chart, Fig. 3(d). The intensities and the band-block steps that are mentioned above are subjective and solely depend on the effective f-number of the Fourier transform lens that is used and also on the concentration of the sample. However, for a given system, the results are reproducible.

 

Fig. 3. Experiment results demonstrating the continuous band-block processing of grating chart. Images are captured by CCD camera at various input intensity (a) 0.02 mJ, (b) 0.05 mJ, (c) 0.47 mJ, and (d) 0.7 mJ.

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The image processing technique demonstrated can be adapted for early detection of microcalcifications in breast cancer diagnostics [19]. The microcalcifications (tiny calcium deposits in human breast) correspond to high spatial frequencies in the Fourier spectrum because of their small size and diffuse nature. The test objects in the above experiments can be replaced with both analog screen-film and digital mammography images. The main advantage of applying the present technique to the mammograms lies in the continuous band-block filtering. Abnormalities detected in mammography are classified as spiculated masses, stellate lesions, circumscribed masses and microcalcifications. These abnormalities may vary in size and intensity and hence correspond to different spatial frequencies in the Fourier spectrum. This technique not only enhances the visibility of microcalcifications it can also selectively display various features of interest to the radiologist.

3. Conclusion

We developed a simple self-adaptive all-optical system that performs image processing and optical power limiting at the same time. The nonlinear absorption characteristics of chromophores are used to manipulate the spatial frequencies at the Fourier plane. The proposed technique is self-adaptive to the background changes in object and requires only a two lenses and a filter for edge enhancement. A novel feature of the technique is variable high pass filtering can be achieved by controlling the incident intensity. For reverse saturable absorbing materials, the proposed technique opens new areas of photonic applications.