CTIS Function

CTIS Function

    The computed tomography imaging spectrometer (CTIS) is a non-scanning instrument capable of simultaneously acquiring full spectral information (450 nm to 750 nm) from every position element within its field of view (75 mm C 75 mm).  The current spatial and spectral sampling intervals of the spectrometer are 1.0 mm and 10 nm, respectively.  This level of resolution is adequate to resolve signal responses from multiple fluorescence probes located within individual cells or different locations within the same cell.  Spectral imaging results are presented from the CTIS combined with a commercial inverted fluorescence microscope. Results demonstrate the capability of the CTIS to monitor the spatiotemporal evolution of pH in rat insulinoma cells loaded with SNARF-1.  The ability to analyze full spectral information for 2D (x,y) images allows precise evaluation of heterogeneous physiological responses within cell populations.  Due to low signal levels, integration times up to 2 seconds were required. However, reasonable modifications to the instrument design will provide higher system transmission efficiency with increased temporal and spatial resolution. Specifically, a custom optical design including the use of a larger format detector array is under development for a second generation CTIS. 

    The raw image collected by the CTIS consists of 49 diffraction orders associated with the CGH disperser. The 0th diffraction order is located at the center of the image. This order represents a direct view of the spatial radiance distribution in the field stop and exhibits no dispersion. The remaining diffraction orders exhibit dispersion increasing with order number. Reconstruction of the object cube from the raw data requires knowledge of how individual voxels map to the imaging array. Each voxel corresponds to an object volume, measuring DxDyDl, where Dx, Dy, and  Dl are the spatial and spectral sampling intervals, respectively.

Figure 1.  Mapping from a volume element (voxel) within the object cube to CTIS focal plane.

The (x,y.l) object cube is shown in outline. Part (a) shows the diffraction pattern due to a voxel at 450 nm. Part (b) shows the diffraction pattern due to a voxel at 710 nm. Changes in the center wavelength of a voxel result in an expansion or contraction of the diffraction pattern in the focal plane and changes in spatial location result in a corresponding translation of the diffraction pattern in the focal plane. The extent of the CCD array is indicated by the solid-line boundary box. The diffraction patterns are shown in inverted contrast. 

A set of diffraction patterns, such as these is recorded for all voxels in the object cube. The ensemble of diffraction patterns describes the mapping from object space to image space effected by the CTIS. The mapping can be inverted to reconstruct an object cube from a raw image, such as the one shown in Figure 4.

Figure 4. A representative raw image of 6-mm diameter fluorescing microspheres.

A representative raw image of A7R5 (rat smooth muscle) cells loaded with MIM, FTIC, and propidium iodide.  The central order corresponds to an undispersed image of the cells. The raw image measures 1,024 1,024 pixels.  The cells measure approximately 70-100 mm in length and 25 mm in width.  The image was taken using a 40, NA = 1.35, oil-immersion objective and an integration time of 2.2 sec. (b) 

Instrument Modeling

    The CTIS instrument is modeled as a linear imaging system and as such can be described in terms of linear algebra.  The 2D image (see Figure 2) and the 3D (x, y, l) object cube are re-organized as vectors, g and f, respectively.  These vectors are related to each other by means of a system matrix, denoted by H. The matrix H can be acquired experimentally by recording calibration images, such as those shown in Figure 2, for every voxel within the object cube. (Descour et al., 1997).   As a result of the shift-invariance, only a single calibration image per wavelength band needs to be acquired and stored (Volin et al., 1998).  As arbitrary calibration images are needed during reconstruction of the object cube, the stored calibration images are recalled and shifted to the necessary spatial position. 

    The reconstruction of the 3D object cube is performed using the Multiplicative Algebraic Reconstruction Technique (MART).  The iterative progression from the kth estimated object cube, , to the (k + 1)st occurs according to the equation 

 The initial estimate of the object cube is spatially and spectrally uniform.  Reconstruction tests performed in conjunction with a non-imaging reference spectrometer determined the number of iterations yielding the optimum accuracy in the reconstructed spectra.  Typically, seven or eight iterations performed best. Therefore, the results presented in the next section were obtained after eight (8) iterations of the reconstruction algorithm. Each iteration required approximately 22 seconds to complete on a 450 MHz Pentium II personal computer for 75x75 spatial resolution elements and 30 spectral bands. Currently, the initial estimate for the algorithm corresponds to a spectrally and spatially uniform field.  Use of an estimate that more closely resembles the object would provide a more accurate reconstruction in fewer iterations.  This can be accomplished by using an estimate, which is spatially identical to the zero order image and spectrally uniform.

CTIS Layout

    The CTIS microscope consists of two optical subsystems: an interchangeable fore-optics subsystem and the CTIS subsystem. Within the context of this paper, the fore-optics subsystem consists of a standard inverted fluorescence microscope (Olympus IMT-2) equipped with a 100 W Hg lamp as the illumination source. The CTIS subsystem includes a field stop, collimator and re-imaging lenses, a computer-generated-hologram (CGH) disperser, and a CCD detector array. The CTIS is constructed with commercial optics, with the exception of the CGH disperser.   An eyepiece at the side photo port of the microscope forms the intermediate image at the field stop of the CTIS subsystem.  Thus, a single imaging eyepiece is the only requirement for adapting the CTIS to a standard microscope.

Collaborators :

Ronald M. Lynch
Department of Physiology
University of Arizona
Tucson, Arizona
 
Arthur F. Gmitro
Departments of Radiology and  Optical Sciences
University of Arizona
Tucson, Arizona
 
A.J. Gandolfi
Department of Anesthesiology
University of Arizona
Tucson, Arizona
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