Micropolarizers in Real Time Polariscope Petr KUCERA, Friedemann MOHR

EO & Laser Metrology Lab, Hochschule Pforzheim University, Tiefenbronner Straße 65, 75175 Pforzheim, Germany

petr.kucera@hs-pforzheim.de, friedemann.mohr@hs-pforzheim.de

Abstract. This contribution deals with a polariscope, an instrument for determining internal strain in a transparent medium by exploiting its polarization transmission: When a sample of birefringent material is inserted in a polarized beam of light a fringe pattern is observed. The pattern is captured by a camera and processed to reveal internal stresses in the probe. However, in order to completely specify stresses, four patterns obtained under different optical conditions are used. These can be achieved either by using a rotating analyzer in the optical setup or by applying the so called “Multispec Imager” approach where the output beam is divided into several parallel beams which can then be directed to separate sections of a single camera or to several individual cameras.

Disadvantages of the former solution is the requirement of a mechanically rotated component (necessitating a driving motor and longer measurement time whence this concept is far from being suitable for real-time use) and of the latter is its price and higher complexity of the optical layout. The use of micropolarizers in a digital polariscope removes all stated disadvantages, hence such a polariscope processes a single beam (no need of beam-splitting) and one fringe pattern (no need of a rotating analyzer).

Keywords Polariscope, polarization camera, birefringence, dichroism, micropolarizer, superpixel.

1. Basic Unit of Polarization Camera In our approach a CCD camera is combined with a

mask of microstructured polarizers which split the ob-served image such that neighboring camera pixels receive picture portions which have undergone transmissions through differently oriented linear polarizers. Thus, our polarization camera can be regarded as consisting of a number of basic elements where each contains 4 mi-cropolarizers with different transmission axis orientation and which we call a superpixel. In this way 4 phase shifted images are contained in one single image. Hence, the resolution of the polarization camera is given by the size of the superpixel. The basic geometry of our arrangement is shown in Fig. 1(a): Each circle corresponds to one element of the polarizer mask; 4 elements make up one superpixel.

With each CCD pixel adjusted such that it coincides with the center of a polarizer (Fig. 1(a)) we are then able to treat the irradiation within the area of the superpixel as if we had let the irradiation on the superpixel flow through a conventional polarizer which we rotate and read the throughput every 45 degrees. In fact, micropolarizers and CCD sensor simply constitute a rectangular array of micropolarizers with well defined extinctions and trans-mission axes (these parameters are given by the mutual po-sition of micropolarizers and CCD sensor and, of course, by the properties of micropolarizers and CCD sensor it-self).

Fig. 1. Structure of the basic element of a polarization camera:

(a) polarizers and CCD sensor with identical pitch, (b) with CCD pitch doubled.

Fig. 1(a) indicates, as ellipses with spatially varying shape and orientation, the physical origin of its polarization characteristics: The polarizing effect is generated by a modification of the structural properties of silver nanopar-ticles embedded in glass using laser radiation [1]. As can be seen, the micropolarizers’ properties change continually over the area of the superpixel. This is due to the manufacturing technique which causes the originally spherically shaped particles to become needles oriented in the direction of a linearly polarized high-intensity writing laser beam with circular geometry. In the overlapping regions two successive exposures lead to deviations of the desired shape and orientation – and thus to impaired polarization performance.

The 1-by-1 correspondence of polarizers and CCD pixels appearing so straightforward in Fig. 1(a) is modified in Fig. 1(b) by combining the polarizer mask with a CCD sensor with a smaller pitch such that the polarization in the overlap regions can also be utilized. This, however, requires a higher complexity of the interpreting mathematical algorithm and thus, longer calculation time. (The problem of algorithm is though, too exhaustive, and can therefore not be treated in detail here.)

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2. Extinction Measurements The most crucial parameter determining the

performance of polariscopes is the extinction coefficient of the polarizers. In this respect, the novel approach differs considerably from conventional polariscopes where the macroscopic polarizers used have so high extinction that they can be assumed as ideal, i.e. infinity. In contrast, the extinction of microscopic polarizers – remember, it is their use which enables the real-time processing of data – is relatively low. Thence, the processing of captured data from a polarization camera requires an algorithm which takes into account the finite value of the extinction coefficient. For that reason we had to thoroughly investigate the extinction of our polarizers and its physical background.

2.1 Extinction given by scattering Due to the periodicity of the structure (one period is

the superpixel) diffraction occurs. The diffraction orders represent the useful signal (cf. Fig. 2).

In comparison, the light which is scattered through the silver needles making up the polarizer can be understood as noise impairing the extinction coefficient. The typical scattering diagram is shown in Fig. 3. The ratio of the power contained in the diffractive orders and the total power scattered determines the value of the extinction ratio.

Fig. 2. Diffraction due to the periodicity of the micropolarizers.

2.2 Malus law fitting When the linear polarization of the beam passing

through a polarizer is rotated then the detected irradiance has a typical Malus law profile. The extinction coefficient is then determined as a ratio of the curve’s maximum and minimum.

An interesting finding was, in our case, that the extinction periodically depends on the gap distance between the microscopic polarizers and the CCD detector used, cf. Fig. 4. (Such a behavior can not be predicted by the scattering method: the scattering method determines just the main maximum.) The upper curve in Fig. 4

represents measurement with laser light and the lower curve was obtained using a LED source. In this case the rapid decrease of the extinction coefficient is due to the high divergence of the LED source which causes crosstalks.

Fig. 3. Typical scattering diagram of the micropolarizers.

Fig. 4. Extinction dependence on the gap between micro-

polarizer and a CCD sensor.

3. Simulation of Micropolarizers In addition to the experimental investigations we

studied the performance of the micropolarizer field theoretically by applying two simulation approaches.

For the first simulation we used a software program called ASAP. This program uses two mathematical concepts: With the first one, the paraxial field is decomposed into Gaussian beams and these are then propagated. This method fails when the field propagates through microstrucures with dimensions on the order of the wavelength. With the second technique (called beam propagation method (BPM)) the finite difference technique is applied to solve the semivectorial Helmholtz equation. This technique can, however, not be used for a medium causing polarization coupling (i.e., the birefringence axes of the medium do not coincide with the reference frame).

In the second simulation approach we used the finite difference approach to directly solve Maxwell’s equations. This approach is able to analyze anisotropic and inhomogeneous periodic structures. A description of the method can be found in [2].

3.1 Gaussian beams technique We used this technique primarily to study effects due

to two different arrangements of the superpixel. The injected field, which is needed to make an experimental observation and to set the initial conditions, was linearly polarized. In Fig. 5 (left) the irradiance pattern in the plane immediately after the field of micropolarizers is shown with a symmetric arrangement of the polarizers in the su-perpixel (i.e., with orthogonal micropolarizers liying diago-nally, cf. the inset). The experimental figure was obtained by imaging the micropolarizers on a CCD sensor with a sufficiently high magnification such that the discrete nature of CCD pixels did not considerably influence the image. Fig. 5 (right) shows the respective calculation results by the Gaussian beams technique.

Fig. 5. Irradiance pattern after the symmetric structure when horizontally polarized light was injected (left – measurement, right – simulation).

Next we imaged and simulated micropolarizers with a non-symmetrical structure of the superpixel (the orthogonal micropolarizers are placed side by side, cf. inset in Fig. 6 left). A comparison of both experimental and theoretical results with Fig. 5 clearly shows that the non-symmetrical approach gives much worse contrast. Obviously, diffraction effects strongly spoiled the image. Or, in brief: For the extinction achieved, the symmetrical arrangement is much superior to the non-symmetrical one.

Fig. 6. Irradiance pattern from the non-symmetric superpixel.

3.2 Finite difference technique It is generally known that for a periodic structure it is

sufficient to model just one period by applying periodic boundary conditions. This is made by forcing the field to have same values at the periodic boundaries.

Let us consider the geometry in Fig. 1(a) and let denote the lower diagonal x with the origin in the third circle (third micropolarizer). This x axis goes through the middle of the second circle and then reaches a micropolarizer with the same properties as the third one

(not shown in the figure). Hence the permittivity tensor describing the medium continuously changes over x. The propagation direction coincides with the normal to the surface of the micropolarizers and is denoted as z (the thickness of the micropolarizers). Fig. 7 shows electrical field components and power flow in z-x plane for the incident beam linearly x polarized.

The waveform deformation is due to the birefringence (the medium possessed both, birefringence and dichroism). The appearance of y component of the field is due to the non-diagonal terms of the permittivity tensor which produce coupling between the field components and the appearance of z component (diffractive orders) is due to the change of the medium properties in the transversal direction.

Fig. 7. Electric fields components and power flow in one period

of the micropolarizer structure.

4. Retardation Measurement Examples In order to demonstrate the character of results

achieved with our micropolarizers-based polarization camera we show the CCD picture (Fig. 8) taken from a strain disc (a photoelastic plate subjected to lateral squeeze so to generate an inner strain with related optical retardation) and the image processing results acquired therefrom (Fig. 9).

The commonly used algorithms in the image proc-essing part of a digital polariscope are based on several phase shifted images which in our case are contained in a single image. For a review of such algorithms see [4]. The algorithm which we developed differs from the conven-tional algorithms by taking into account the finite value of the extinction coefficients of the micropolarizers. However, in the case of micropolarizers the extinction depends on the properties of both components of the polarization camera: the CCD sensor and the micropolarizers. These properties also include the pitches of both components and their mutual alignment. All these effects need to be well understood to be able to take them into account accordingly in the mathematical processing algorithm.

Fig. 8. A picture of a strain disc taken from a polarization

camera.

For a demonstration of the accuracy achieved so far for a particular optical layout and image processing algorithm we present a retardation measurement (Fig. 10(a)) of a special model exhibiting a retardation that varies linearly over one lateral dimension of its aperture. (Such a device is known under the name Babinet – not Soleil-Babinet (!) - compensator). The accuracy can be estimated as the deviation from the linearity of the curve depicted in Fig. 10(b).

Fig. 9. Measured retardation of a strain disc.

5. Conclusion In this contribution it was shown that an arrangement

of suitably manufactured micropolarizers can be used with good success in polarimetry: Combined with a CCD camera it makes possible real-time determination of plane stresses in a transparent probe like flat glass or glass containers. The high measurement speed possible with this approach enables 100% quality inspection in the glass manufacturing process. This promises much higher product quality as the manufacturing process can be controlled much better and, at the same time, energy waste can be reduced considerably.

a)

b)

Fig. 10. Measured retardation of Babinet compensator with the orientation of its slope tilted by 0° as referred to the horizontal. ordinate: pixel no., abscissa: retardation in degrees.

Acknowledgements Research described in the paper was financially

supported by the German grant organization VDI under the project No. 103N10485 (Bildgebendes Echtzeit-Polarimeter mit Mikrostrukturierten Polarisatoren).

Special thanks are expressed to A. Volke and A. Stalmashonak from the CODIXX company which provides us with the samples of micropolarizers and to M. Rank and H. Katte from the Ilis company which is specialized for innovative polariscope measurements.

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[2] OH, Ch., ESCUTI, M. J. Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation. Optics Express 11871, 2006, vol. 14, no. 24.

[3] ASUNDI, A. K. Matlab for photomechanics: A primer. Elsevier, 2002.

[4] ASUNDI, A. K., TONG, L., CHAI, G. B. Dynamic phase shift photoelasticity, Applied Optics, 2001, vol. 40, p. 3654-3658.

[5] GUO, J., BRADY, D. J. Fabrication of high-resolution micropolarizer arrays, Optical Engineering, 1997, vol. 36, no. 8, p. 2268-2271.