1. Field of the Invention
The present invention relates to an imaging polarimetry in which, and an imaging polarimeter with which, a two-dimensional spatial distribution of a state of polarization of light under measurement is measured by the use of a birefringent prism pair.
2. Description of the Related Art
Light has properties of a “transverse wave”. Based upon the premise of three mutually orthogonal axes (x, y, z), when a propagation direction of light is assumed to be the z-axis direction, a vibration direction of the light is a direction along the x-y plane. The vibration direction of the light within the x-y plane has a bias. This bias of light is referred to as “polarization”. A biased state of light is referred to as a “state of polarization (SOP)” in this specification. Typically, the SOP varies depending upon positions (coordinates) in the two-dimensional x-y plane.
When light in some state of polarization is incident on an object under measurement to acquire emitted light such as transparent or reflected light and the object under measurement has optical anisotropy to the light, a change in SOP is observed between incident light and emitting light. Acquiring information on anisotropy of the object under measurement from the change in SOP is referred to as “polarimetry”. It is to be noted that causes of such anisotropy may include anisotropy of a molecular structure, presence of stress (pressure), and presence of a local field and a magnetic field.
A measurement in which a change in SOP between the incident light and the emitted light is obtained with respect to each position (coordinates) of the two-dimensional x-y plane and then to acquire information on anisotropy of the object under measurement is especially referred to as “imaging polarimetry”. This imaging polarimetry has an advantage of acquiring a great amount of information as compared to the case of measurement at a point or in a region averaged by a face in the x-y plane. In the imaging polarimetry, a device for measuring an SOP of emitted light (occasionally, incident light), namely an imaging polarimeter, is a key device.
As fields of application of the imaging polarimetry known are the field of an inspection of optical electronics, the medical field, the remote sensing field, the machine vision field and the like. In the field of the inspection of the optical electronics, for example, since birefringence or a defect due to residual stress can be measured in a nondestructive and non-contact manner, the imaging polarimetry has been applied to an inspection or study of a liquid crystal, an optical film, an optical disc, and the like. In the medical field, an attempt has been made for early detection of glaucoma or a cancer cell since several kinds of cells have polarization properties. In the remote sensing field, an inclination or the degree of flatness of an object under measurement can be measured from the two-dimensional spatial distribution of the state of polarization by remote control and for example, the imaging polarimetry is applied to an examination in vegetation. In addition, in the machine vision field, for the same reason, a configuration of an object is recognized from a polarization image.
Incidentally, assuming that light traveling in the z-axis direction exists, polarized light in a state where a vibration component in the x-axis direction is perfectly correlated (synchronized) with a vibration component in the y-axis direction is classified into three types: linearly polarized light, elliptically polarized light, and circularly polarized light. Parameters for expressing a state of elliptically polarized light are: ε for an ellipticity angle, θ for an azimuth angle, Δ for a phase difference, and Ψ for an amplitude ratio angle.
Further, as parameters for effectively expressing a degree of polarization of light, the ellipticity angle, the azimuth angle and the like, Stokes Parameters are used. The Stokes Parameters are composed of four parameters having definitions as follows:
S0: total intensity
S1: difference between intensities of linearly polarized components with angles of 0° and 90°.
S2: difference between intensities of linear polarized components with angles ±45°.
S3: difference between intensities of left and right circularly polarized light components.
In a three-dimensional space where the three mutually orthogonal axes are taken as S1, S2 and S3, assuming a sphere with a radius S0 and an original point of the axes taken as a center, an SOP of arbitrary light is expressed as one point in this three-dimensional space and a degree of polarization is expressed by the following expression:
                              Degree          ⁢                                          ⁢          of          ⁢                                          ⁢          polarization                =                ⁢                  (                      distance            ⁢                                                  ⁢            from            ⁢                                                  ⁢            original            ⁢                                                  ⁢            point            ⁢                                                  ⁢            to            ⁢                                                  ⁢            point                    ⁢                                                                                ⁢                              (                                          S                1                            ,                              S                2                            ,                              S                3                                      )                    /                      S            0                                                  =                ⁢                                            (                                                S                  1                  2                                +                                  S                  2                  2                                +                                  S                  3                  2                                            )                                      1              /              2                                /                      S            0                              
It may be understood from the above that in the case of a perfectly polarized light (degree of polarization=1), one point expressing the SOP exists in the sphere with a radius S0. Further, the ellipticity angle and the azimuth angle respectively correspond to halves of a latitude and a longitude of the one point expressing the SOP in the above three-dimensional space. As thus described, it is possible to express all information on the SOP if the four parameters S1, S2, S3 and S0 of the Stokes Parameters can be obtained.
As conventionally prevailing imaging polarimetries, a rotating-retarder polarimetry and a polarization-modulation polarimetry are known.
In the rotating-retarder polarimetry, a retarder and an analyzer intervene in sequence in a channel for light under measurement toward an imaging device. Here, the retarder is an optical element having two principal axes (fast axis and slow axis) in mutually orthogonal directions, and is also configured to change a phase difference between the two principal axes before and after passage of light. Further, the analyzer is an optical element having one principal axis and also is configured to allow transmission of only one linearly polarized light component corresponding to the direction of the principal axis.
In this rotating-retarder polarimetry, for obtaining two-dimensional spatial distributions of the four Stokes Parameters independently, it is necessary to physically rotate a retarder itself and take an intensity distribution measurement for at least four kinds of directions. Namely, the Stokes Parameters of incident light are expressed as functions S0(x, y), S1(x, y), S2(x, y), and S3(x, y) of two-dimensional spatial coordinates.
In the polarization-modulation polarimetry, two retarders (first retarder and second retarder) capable of electrically controlling a phase difference and one analyzer intervene in sequence in a channel for light under measurement toward an imaging device. Among such retarders used are an electro-optic modulator, a liquid crystal and a photoelastic modulator. For example, a phase difference of 45° is set between the principal axes of the first retarder and the second retarder.
Also in this polarization-modulation polarimetry, for obtaining two-dimensional spatial distributions of the four Stokes Parameters independently, it is necessary to vibrate, by electric control, a phase difference between the first retarder and the second retarder in a predetermined angle range to obtain a plurality of intensity distributions.
However, concerning the conventional general imaging polarimetry typified by the rotating-retarder polarimetry and the polarization-modulation polarimetry, the following problems have been pointed out.
(1) First Problem
Since a mechanical or active polarization controlling element is required, there are problems including that: [1] a problem of vibration, heat generation and the like are unavoidable; [2] the degree of size reduction is limited due to necessity for a mechanical element and the like to have some capacity; [3] a driving device for consuming electric power is essential; and [4] maintenance is necessary and complex.
(2) Second Problem
Since it is necessary to repeatedly measure a plurality of intensity distributions while changing conditions of the polarization modulating (controlling) element, there are problems including that: [1] measurement takes relatively long; and [2] an object under measurement needs to be kept stable during measurement.
In order to solve the above problems with the conventional general imaging polarimetry, the present inventors and the like developed, in advance, an “imaging polarimetry using a birefringent prism pair” (refer to T. Kaneko and K. Oka, “Measurement of spatial two-dimensional distribution of polarized light state using birefringent wedge,” The 49th Extended Abstracts, Japan Society of Applied Physics and Related Societies (Japan Society of Applied Physics, Hiratsuka, 2002) p. 977 and K. Oka and T. Kaneko, “Compact complete imaging polarimeter using birefringent wedge prisms,” Opt. Express, Vol. 11, No. 13, pp. 1510-1519, 2003).
A constitutional view of an experiment system for explaining the imaging polarimetry using the birefringent prism pair is shown in FIG. 19. As apparent from this figure, light projected from a helium-neon laser 1 is enlarged in its beam diameter by collimator lenses 2 and 4 and a pinhole 3 and transmitted through a polarizer 5 and a twisted nematic liquid crystal 6, to obtain a light wave having an SOP depending upon the position (coordinates) of the two-dimensional x-y plane. Two-dimensional spatial distributions S0(x, y), S1(x, y), S2(x, y) and S3(x, y) of the Stokes parameters of the light wave are obtained by a measurement system 7 surrounded with a broken line in the figure.
Light under measurement is first transmitted through an imaging lens 8, and through two birefringent prism pairs BPP1 and BPP2 and a flat-plate analyzer A in sequence, and then incident on a CCD imaging element 9. The image lens is used in order to forms an image of a projection surface of the twisted nematic liquid crystal 6 on the CCD imaging element. Meanwhile, the two birefringent prism pairs BPP1 and BPP2, and the flat-plate analyzer A are overlapped on a front face of the CCD imaging element. (The surfaces of BPP1 and BPP2 and A may be focused on the front surface of the CCD imaging element optically in the use of a relay lens and the like. The birefringent prism pair comprises a pair of wedge-shaped prisms formed of a birefringent medium and alternately overlapped with each other. A contact surface of each of the two birefringent prism pairs BPP1 and BPP2 is inclined at a fine angle with respect to x axis and y axis. Here, two principal axes of the birefringent prism pair BPP1 agree with the x and y axes, while two principal axes of the BPP2 are inclined 45° from those. Here, a transmission axis of the analyzer A is arranged in parallel to the x axis.
In each of the two birefringent prism pairs BPP1 and BPP2, a phase difference created between the orthogonal polarized light components depends upon two-dimensional spatial coordinates. Hence, as shown in FIG. 20, an intensity distribution including three carrier components is obtained from the CCD imaging element 9. An amplitude and a phase of each of the carrier components are modulated by the two-dimensional spatial distribution of the Stokes Parameters of the light under measurement. It is therefore possible to obtain each of the Stokes Parameters by execution of a signal processing with a computer 10 by the use of Fourier transformation.
One example of results of an experiment is shown in FIG. 21. This is a result obtained in the case of uniformly applying an electric field to only a part of a transparent electrode of a character “A” in the twisted nematic liquid crystal 6. Both right and left figures show two-dimensional spatial distribution θ (x, y) of the azimuth angle and two-dimensional spatial distribution ε (x, y) of the ellipticity angle which are calculated from the two-dimensional spatial distribution of the Stokes parameters, respectively. It is thereby understood that an SOP depends upon two-dimensional spatial coordinates.
As thus described, according to the imaging polarimetry using the birefringent prism pair, it is possible to obtain the two-dimensional spatial distribution of each of the Stokes Parameters by a frequency analysis of properties of the intensity distribution. It is reasonably necessary to obtain respective retardations of the two birefringent prism pairs BPP1 and BPP2 prior to the frequency analysis. Here, retardation means a phase difference created between linearly polarized light components along the two orthogonal principal axes.
According to the foregoing imaging polarimetry using the birefringent prism pair, advantages can be obtained including that: [1] a mechanically movable element such as a rotating retarder is unnecessary; [2] an active element such as an electro-optic modulator is unnecessary; [3] four Stokes Parameters can be obtained from one intensity distribution at once so that a so-called snap shot measurement can be performed; and [4] the constitution is simple, and thus suitable for size reduction.
However, concerning the foregoing imaging polarimetry using the birefringent prism pair, a problem of generation of a relatively large measurement error has been pointed out for the following reasons.
(1) Variations (Fluctuations) in Retardation of the Birefringent Prism Pairs BPP1, BPP2 
Retardation of the birefringent prism pair varies sensitively due to a temperature or pressure change, resulting in that the phase of the intensity distribution detected by the imaging element varies due to the temperature or pressure change, as shown in FIG. 22. Consequently, as shown in FIG. 23, the temperature or pressure change causes generation of an error in a measured value of the Stokes parameter obtained from the intensity distribution. In addition, although only the x surface is shown in FIGS. 22 and 23 for the sake of simplicity, the same is said in the y direction.
(2) Displacement in Relative Position between the Birefringent Prism Pair and the Imaging Element
In a system to which a relay lens is inserted between the birefringent prism pair and the imaging element, relative positional displacement between both of them causes a large error factor. When the coordinates on the birefringent prism pair to be sampled by each pixel of the imaging element is displaced due to the vibration every measurement, as shown in FIG. 24, a state is generated which is equivalent to a case where retardation of the birefringent prism pair varies, resulting in generation of an error in a measured value of the Stokes parameters obtained from the intensity distribution. In addition, although only the x surface is shown in FIG. 24 for the sake of simplicity, the same is said in the y direction.
Incidentally, for example, in the inspection of the optical electronics, accuracy required in a two-dimensional spatial distribution of an ellipticity angle or an azimuth angle is considered to be an error in the order of not larger than 0.1°. When this accuracy is to be realized by stabilizing retardation of the birefringent prism pair, it is necessary to keep a variation in temperature of the birefringent prism pair at or under 0.5° C.
However, it requires a large-sized temperature compensating device such as a heater or a cooler for the temperature stabilization, which unfavorably causes a loss of advantages (size reduction, non-inclusion of an active element, etc.) of the imaging polarimetry using the birefringent prism pair. Hence it is practically difficult to reduce a measurement error by stabilizing the retardation of the birefringent prism pair.
In addition, in the system to which the relay lens is inserted, it is practically difficult to prevent the vibration so that the relative displacement between the birefringent prism pair and the imaging element become negligible in the applied field in which the polarimeter has to be provided on a mobile body such as the remote sensing or the robot vision field.
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