Applied Optics, nuigalway, David Lara's research

Conventional imaging systems can only be used to record the intensity of light that has been scattered from the object under observation. Hence, some biological tissues and materials appear to be homogenous even when they may possess some kind of internal structure. In some tissues, such as muscle, tendon, the human cornea, and the retina, the assessment of the state of these structures can be a valuable tool in determining the overall health of the biological sample. The human retina, for instance, consists of several layers of different types of cells through which light must pass before reaching the photoreceptors layer. These first layers are transparent in order to maximize the light flux falling onto the photoreceptors, and in regions around the fovea and the head of the optic nerve, some layer elements are arranged radially from the centre of each of these two spots. This sort of arrangement, where transparent fibres are immersed in a medium of different refractive index, produces form birefringence [1]. In this work we introduce a new technique to obtain polarisation sensitive three-dimensional images, which we expect can reveal the anatomical condition of living tissue that possesses polarisation-dependent signatures.

The centre part and the novelty of our project is the combination of a complete Mueller matrix ellipsometer with a confocal microscope. We are developing an instrument that we expect will be capable of measuring the complete Mueller matrix of contiguous optical slices of a biological sample.

We built a division-of-amplitude Mueller matrix ellipsometer similar to the one used by F. Delplancke in 1997 [2]. A schematic diagram of the setup with the modifications we implemented is shown in Fig. 2. The state of polarisation of the light incident on the sample is modulated using two Pockel's cells. We measure simultaneously the 4 components of the Stokes vector of the light that is scattered from the sample and then passes through a confocal imaging system. For these measurements we use four different polarisation analysers (linearly horizontal, vertical and 45 degrees, and right-circular). We record the 4 modulated signals and use Fourier analysis to obtain the 16 Mueller matrix elements of the sample.

Fig 2. Division-of-amplitude confocal ellipsometer: wavelength, 532 nm; modulation, sawtooth signals of 312.5 and 156.25 Hz; retardance amplitudes, both equal to half a wavelength; detector sampling frequencies, 40 kHz (photo).

Fig 3. Modulated retardances (left) and the resulting polarisation states generated repesented on the Poincare sphere(right). The green dots on the sphere correspond to the combination of a vertical pair of dots on the retardances graph.

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Fig 4. Raw detected signals and the Fourier series coefficients for each detector. Blue stars and red circles represent the cosine and sine fourier coefficients respectively.

3. Double-pass eigenvalue calibration - modified from [3]

For the calibration of the double-pass ellipsomeer we implemented a modified version of the eigenvalue calibration method (ECM) described previously by Compain et al [3]. Results show that the modified ECM can be applied in a douple-pass configuration with the only assumption being that the Mueller matrix of a 99.9% reflectivity mirror is known.

The following results show the validity of the claibration method. We took five measurements of the Mueller matrices of a polariser oriented at 45 degrees and the same retarder used for the calibration but oriented at 45 degrees instead of 30 degrees. The mean values of the Mueller coefficients, the standard deviation matrix and the theoretical representation of the samples are shown in Fig. 5.

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Fig 5. Experimental vs theoretical values of the Mueller matrix of a polariser and a retarder at 45 degrees using the confocal ellipsometer (std stands for the standard deviation of 5 measurements).

Performance

Fig 6. Theoretical vs experimental values of the Double pass Mueller matrices of 5 different samples (Air, linear polariser at 0, 89.5 and 45 degrees and a third order 633nm Quarter wave retarder at 30 degrees). Bars on the left represent theoretical values and bars on the rigth the experimentally measured values. Standard deviation of 5 measurements are indicated as error bars between the corresponting graph bars.

4. Axially scanned results - First time achievement

The first sample we measured using the confocal Mueller matrix ellipsometer was a mirror that was scanned along the optical axis. This was done at increments of 5 microns and 10 microns for two different confocal pinhole diameters of 25 and 50 microns, respectively. The results show an asymmetric axial Mueller matrix - PSF that not only corresponts to the typical mueller matrix of a mirror at the best point of focus. A clear linear retardance is apparent in the graph which can be due to a misalignment in the objective lens. The objective lens was not in place when the calibration method was performed. The small working distance of the objective lens was not suitable for the calibrating samples we used. The asymmetry of the curves with respect to the plane of best focus is most ceirtainly due to spherical aberration in the system, see [4].

Fig 7. Axially scanned Mueller matrix of a dielectric mirror using two different pinhole sizes. Data points represent the mean of 3 measurements. The error bars displayed on the graphs show the standard deviation and in most cases they are smaller than the size of the point marker (Click on image to get pdf).

We then put a stack of 3 quarter wave retarders (for 560 nm) between two glass plates as it is shown in figure 8, and measured the Mueller matrix of planes separated every 10 microns through the sample. The results are shown in figure 9. Please note that due to the sample characteristics it is only the signal that is reflected at the interfaces that can be used for polarisation analysis, but it was necessary the high resolution scanning in order to assure that reflection from each surface was to be measured.

StackPhoto StackPict

Fig 8. Stack of retarders between two glass plates.

Fig 9. Depth-resolved Mueller matrices of measured planes through the stack sample. The first reflecting surface appears on the left of the graphs (Click on image to get pdf).

Fig 10. Unit reflectivity depth-resolved Mueller matrices of measured planes through the stack sample. This normalisation results in the changes between the interfaces matrices being due to polarisation only and not intensity fluctuations (Click on image to get pdf).

Retardance RetAngle DepPower

Fig 11. Retardance, linear retardance azimuth angle and depolarisation power at each interface. Values were calculated based on polar decomposition as explained in [5].

5. Remarks

We have introduced the combination of a depth-resolved confocal imaging system with a complete Mueller matrix ellipsometer. Since the elements of the Mueller matrix that represent a sample are in general linearly independent, polarization sensitive imaging is a 16-dimensional imaging technique that includes intensity as one dimension. we are on the proces of acquiring 3-D polarisation sensitive images from biological samples which is in fact equivalent to developing a 3*16 dimensional imaging device.

Despite the evident repeatability of the measurements, we are certain that optical quality of samples plays a significant role on the accuracy of the measurements. One of the advantages of this type of ellipsometer is the possibility of obtaining high speed measurements. With the assistance of Adaptive Optics, this important feature may allow this technique to be implemented on clinical devices such as a Confocal Laser Scanning Ophthalmoscope.

References

[1] H.B. Klein and G. J. van Blokland, J. Opt. Soc. Am. A, 5, 49-57 (1988)
[2] F. Delplancke, Appl. Opt., 36, 5388-5395 (1997)
[3] E. Compain, S. Poirier, B. Drevillon, Appl. Opt, 38, 3490-3502 (1999)
[4] James B. Pawley, editor, Handbook of Biological Confocal Microscopy, Plenum Press, 2nd edition (1995)
[5] Shih-Yau Lu and Russel A. Chipman, J. Opt. Soc. Am. A, 13 (5), 1106-1113 (1996)