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We proposed to develop microscopies for the rapid measurement of optical rotation tensors of crystals. Previously, measurements of OR tensors have required large, well cut, polished crystals whose preparation was slow and laborious. Our microscopes will examine small, as-grown crystals, thereby rapidly expanding the set of substances amenable to polarimetric analysis. Small crystals will greatly diminish the withering effects of linear birefringence that have long confounded measurements of OR in anisotropic media. Originally, we had proposed the construction of a so-called HAUP microscope.¹ HAUP stands for high accuracy universal polarimetry. As the work developed, we took a second tack, the design and construction of a Mueller matrix microscope. A Mueller matrix microscope can in principle measure all of the crystal optical properties of anisotropic media. To date, Mueller matrix microscopy has been applied to problems in biomedicine, turbid media, liquid crystal display components, and even to the analysis of a magnetic fluid, but there are no applications in crystallography to the best of our knowledge, a yawning gap and a terrific opportunity. During the first year we have constructed both devices. During the upcoming year, we will apply them to the measurement of tensors.

HAUP Microscope

The HAUP-microscope was constructed as proposed so that it could function as an add-on to a standard polarized light microscope. A miniature rotating polarizer unit was built to fit standard microscopes. These units can be added, changed, or removed easily enabling the microscope to be configured for several different applications that accompany measurements of optical rotation via HAUP.

1)With only one rotating linear polarizer and incident circular polarized light one measures linear birefringence and linear dichroism.

2)Without the rotating polarizer after the sample the system measures circular dichroism or more general circular extinction which complements optical rotation measurements.

3)With both rotating polarizers but no circular polarizer the system measures optical rotation. This is the main modus of operation. The sample is placed inside the microscope between two of these polarizers. The modulation of the polarizers allow the derivation of the optical properties we are after. The mechanical details and driver software for the new HAUP microscope have been finished. Further work includes programming a user interface and moving the device into practice. First results of this will be published soon.

Mueller Matrix Microscope

Mueller matrix microscopy (MMM) analyzes the polarization properties of a sample in terms of the transformation of an input Stokes vector (S_in) via the Mueller matrix (M): S_out=MS_in. S_out is the output Stokes vector. A MMM is a crossed polarizer microscope with two rotating quarter wave plates added above and below the sample that act as a complete PSG/PSA pair.² By collecting images as a function of rotations of the PSA and PSG, we can solve the M of a sample at each pixel through pseudo-inversion. A MMM generates sixteen images, each representing one of the elements of the 4´4 Mueller matrix expressed in terms of measurable input and output polarization state intensities.       Unfortunately, the 16 images are not simply related to the fundamental optical constants of interest: absorbance (A), linear birefringence (LB), linear dichroism (LD), circular birefringence (CB), and circular dichroism (CD). To achieve a separation of the convolution of optical properties, we have implemented a differential analysis. The differential Mueller matrix m can be obtained numerically by a approximating the logarithm of matrices. The process of deriving the differential matrix m unfolds the convolution of linear and circular anisotropies so that each fundamental quantity has a unique place in the matrix.³       A Mueller matrix microscope was constructed of a 532 nm Nd:YAG laser, a rotating optical diffuser (glue stick), two linear polarizers, two achromatic quarter wave plates mounted in rotation stages, and a digital camera.        To date, the MMM has worked perfectly with chiral samples having zero or very small linear anisotropies such as NaClO₃ crystals, and a ferroelectric LC that separated into enantiomorphous domains⁴ (sample courtesy of Prof. David Walba, University of Colorado, Boulder). During the upcoming year, we must increase the anisotropy of the crystalline samples under investigation so that we can define the chiroptical sensitivity of instrument.

References

1.  Kaminsky, W.; Claborn, K.; Kahr, B. Chem. Soc. Rev. 2004, 514-535.

2.  Azzam, R. M. A. J. Opt. Soc. Am. 1978, 68, 1756-1767.

3. Chipman, R. A. in Handbook of Optics II, (Ed. Bass, M.) McGraw-Hill, New York,  1994.

4.  Keith, C.; Reddy, R. A.; Hauser, A.; Baumeister, U.; Tschierske, C. J. Am. Chem. Soc. 2006, 16, 3051-3066.