The steady-state solution of the Green’s function obtained by the P3 equation in a semi-infinite medium is presented, the proposed solution is a diffusion-based model. Two time-domain solutions are established: one is the solution under extrapolation boundary condition, which we call the optical parameter method, and the other corresponds to the diffusion equation, which we call the double-diffusion coefficient method. The spatial-resolved reflectance and the time-resolved reflectance are calculated. The Monte Carlo simulation is used to verify the P3 equation. The results show that the P3 steady-state equation and the two time-domain equations are in good agreement with the Monte Carlo simulation. In the steady state, when the distance between the detector and the light source is less than several free paths, the P3 equation is more accurate than the diffusion equation. In other cases, the P3 model and the diffusion model have similar results. However, when the absorption coefficient is large, P3 is more accurate. In the time domain, the optical parameter method is more accurate, and the double-diffusion coefficient method is more consistent with the diffusion equation.
Light transport model has great potential in medical diagnosis and therapy because of the non-invasive nature of
light and the selectively poisonous effect to tumors of photodynamic treatment Light transport model must be
understudied for basic research and clinical application of biomedical optics., many investigators only study the diffusion
equation of matched medium, they take the tissue as the same refractive index. In fact, A tissue is multi-layered
mismatched medium, In order to understand the light transport in tissue,The frequency domain analytical solutions of the
diffusion equation for photon migration through highly scattering a n-layered mismatched medium have been obtained.
The effect of the refractive-index mismatch is taken into account, and the extrapolated boundary condition has been
considered. At the same time, the phase in different situation is calculate use the model.
Near-IR radiation has great potential in medical diagnosis and therapy because of the non-invasive nature of light
and the selectively poisonous effect to tumors of photodynarnic treatment. Therefore, Near-IR light propagation in highly
scattering biological tissue must be understudied for basic research and clinical application of biomedical optics. A tissue
is multi-layered mismatched medium, but many investigators only study the diffusion equation of matched medium. they
take the tissue as the same refractive index. In order to understand the light transport in tissue, We analyze the diffusion
of photons three-layered mismatched medium and set up the solution of Green's function in frequency domain, we
employ the extrapolated boundary condition to set up a solution of the diffusion equation. At the same time, we utilize
the diffuse equation to calculate the phase in different situation
According to the chromatic theory, the color sensitive characteristic of object, light source are defined in the widely used CIE1964 (X,Y,Z) color space and color difference. Their mathematics formulae are deduced. The two kinds of color sensitive characteristic are studied. The characteristics of the color sensitive characteristic are summarized, The mathematics models of the two kinds of color sensitive characteristic can be utilized in some fields such as computer color matching, simulation standard light source.
According to the chromatic theory, the color sensitive characteristic of light source are studied in the widely used CIE1976L*a*b* color space and color difference. The mathematics formulae of characteristic are deduced. The color sensitive characteristics of D65 and A light source are studied. The general laws of the color sensitive characteristic are concluded. The mathematics models of light source can be used in some fields such as making light source.
On the basis of spectrophotometric color matching, the color difference weight factor is proposed and used in the thesis. The weight factor can be expressed as ωj = {{[(x(λj)]2 + [y(λj)]2 + [z(λj)]2}[S(λj)]2}½ and obtained according to the assumption of Σj(ΔXj)2+(ΔYj)2+(ΔZj)2 -> min, i. e., in the range of visible spectrum it is assumed that the square sum of tri-stimulus value deviation produced by spectrum deviation at each wavelength is minimal.Through comparison with spectrophotometric color matching, we find a new weight factor. The new factor multiplied by the variety of reflectivity is the color difference, which is cause by the difference of reflectivity between standard color and matching color. So we name the weight factor: color difference weight factor. The prediction of computer shows the color difference produced by the weight factor is smaller than that produced by the two weight factors which were designed by Schmid and Strockash.
Hyperspectral image can be analyzed by Convex Geometry Analysis(CGA) method. CGA method can unmix endmembers from hyperspectral image. The endmember proportions of mixed pixels can be calculated in inherent dimensional space, and a proportion image, which is called inherent proportion image, is obtained. The endmember proportions of mixed pixels can be calculated in n-space by the Constrained Least Squares, and a proportion image, which is called CLS proportion image, is obtained. In this paper, the inherent proportion image and CLS proportion image of a 30-band remote sensing image are obtained. The two proportion images are similar. The targets that are smaller than earth surface pixel can be identified by the inherent proportion image.
We analyze the inherent channels of hyperspectral data with convex geometry analysis method. In this paper, a method-Volume Method, which selects the inherent channels of hyperspectral data, is presented. The concept of convexity geometry can be used to great advantage in the analysis of hyperspectral data. Convex simplex and inherent dimensionality concept is discussed on base of convex geometry. A set of 252-band hyperspectral data is applied to testify the Volume Method. The endmember proportions are calculated in the inherent dimensional space whose channels are selected by the Volume Method, compared with Constrained Least Squares Method in 252-space.
This paper used a new method to determining the surface reflectance factor, the linear relationship between Kubelka-Munk Function and concentration is obtained.
Color sensitive functions of object is defined in the widely used CIE1976L*a*b* color space and color difference. Mathematics formulae are deduced. The general law of color sensitive functions is concluded. Mathematics models can be used in some fields such as computer color matching.
We present matrix expression of convex geometry analysis method of hyperspectral data by linear mixing model and establish a mathematic model of endmembers. A 30-band remote sensing image is applied to testify the model. The results of analysis reveal that the method can analyze mixed pixel questions. The targets that are smaller than earth surface pixel can be identified by applying the method.
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