Patent Number: 051990571
Section: summary

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image formation-type soft X-ray microscopic apparatus with high resolving power which is mainly used for observing organisms. 2. Related Background Art X-ray microscopes hitherto proposed are roughly divided into the following four types: (1) A projection enlargement type which has no optical system and in which a sample is placed at a position near an X-ray point source in the divergent pencil of the X-rays generated from the X-ray source, and an X-ray film or a two-dimensional X-ray detector is disposed at a position behind the sample at a distance therefrom. (2) An adhesion type which has no optical system and in which an X-ray source, which supplies a bundle of substantially parallel X-rays, is used, and a resist is caused to adhere as a sample to the X-ray source. In this case, a synchrotron radiation source (referred to as "SR" hereinafter), a plasma X-ray source or an electron beam excitation X-ray source is used as the X-ray source. (3) A scanning type in which an X-ray beam is narrowed into a small spot by an optical system, and the beam and a sample are relatively scanned. In this case, SR is used as an X-ray source, and a Fresnel zone plate (referred to as "FZP" hereinafter), a multilayer film mirror or a total reflection mirror is used as an optical element for narrowing the X-ray beam into a small spot. (4) An image formation type in which X-rays are condensed on a sample by using an X-ray source comprising SR, a plasma X-ray source or an electron beam excitation X-ray source and an optical element such as FZP, a multilayer film mirror or a total reflection mirror, and an image of the sample is formed on a film, a fluorescent plate or a two-dimensional X-ray detector by using the same optical element. High-resolution observation of living organisms cannot be easily made by the above-described conventional X-ray microscopes from the technical viewpoint because the microscopes are insufficiently optimized and applies large amounts of X-rays. Namely, although the projection enlargement type (1) is required to have a high-luminance X-ray point source, exposure for a long time is required because of its insufficient intensity, and dynamic observation is thus difficult. In addition, since the sample must be sliced in order to avoid a deterioration in resolving power caused by the influence of Fresnel diffraction, it is difficult to observe a living sample. Since the adhesion type (2) has no high-resolution detector other than the resist, the development of the resist is necessary, and real time observation is thus difficult. In addition, since the magnification is 1, enlargement observation separately using an electron microscope or the like is required. Further, destructive observation, in which the sample is sliced, is required for avoiding a deterioration in resolving power caused by the influence of Fresnel diffraction in the same way as the projection enlargement type (1). The scanning type (3) has the disadvantage that, since an X-ray source having good directivity is required, a large X-ray source such as SR must be used, and the size of the apparatus is significantly increased. In addition, since the scanning time, i.e., the exposure time, is long for obtaining a desired image, dynamic observation is difficult. Since the image formation type (4) exhibits a low degree of efficiency when FZP is used, a large X-ray source such as SR must be used as a high-intensity X-ray source. In addition, the image formation type (4), which uses a mirror, has a disadvantage in that the resolving power cannot be easily improve, and the size of the optical system is increased. This type is thus insufficiently optimized. SUMMARY OF THE INVENTION It is an object of the present invention to provide an image formation-type small X-ray microscopic apparatus which is capable of dynamically observing a living sample with high resolving power of about 20 nm and minimum X-ray exposure, without the same being fixed and broken. The X-ray microscopic apparatus of the present invention is basically of the above-described image formation type. As shown in FIG. 1, the X rays emitted from an X-ray source are condensed on a sample by a single concave aspherical multilayer film mirror condenser, and an enlarged sample image formed on a two-dimensional X-ray imaging element by using a phase zone plate PZP as an image formation optical system. It is effective to use as the single concave aspherical multilayer film mirror condenser a rotary elliptical multilayer reflecting mirror which has a most simple shape and which can be easily manufactured. A plasma X-ray source using a pulse laser is used as a pulse X-ray source, and laser beams are condensed on a target so that X-rays are generated from a small region of the target. The target is disposed at the first focal point of the rotary elliptical multilayer film reflecting mirror, and the sample is disposed at the second focal point thereof. The apparatus has a system in which the X-rays are monochromatized by the multilayer film mirror, and photon counting imaging is performed by using the X-rays of one pulse generated by excitation from the pulse laser. Specifically, in the photon counting imaging with one pulse, if the wavelength of the X-rays is .lambda. and the spectral width is .DELTA..lambda., the X-ray intensity of the pulse X-ray source is adjusted so that the maximum number n.sub.man of detected photons incident upon the two-dimensional X-ray imaging element is within the following range: EQU 25.ltoreq.n.sub.max &lt;.lambda./.DELTA..lambda. In this case, the pulse width is 1 .mu.s or less, and the pulse X-ray source used has intensity which allows imaging with one pulse. If the number of periods N.sub.c of the layer structure of the multilayer film reflecting mirror is 50 to 400, the X-rays are monochromatized so that the value of .lambda./.DELTA..lambda. is 50 to 400, and the X-rays emitted from the pulse layer X-ray source are condensed on the sample by the rotary elliptical multilayer film reflecting mirror. An enlarged image of the organism sample is formed by the objective optical system comprising the phase zone plate having high efficiency and high resolving power. The wavelength range of the soft X-rays used is 2.3 to 4.4 nm for observing the interior of the organism sample having a thickness of about 10 .mu.m, without the sample being fixed and broken. This wavelength range allows the protein and the lipid in the organism to be recognized as contrast differences and the sample having a thickness substantially the same as the cell thickness to transmit the X-rays. In order to observe a living sample, the apparatus is configured from the following viewpoints: (a) Since the path of the X-rays is under vacuum, the sample is observed in a state wherein it is received in a container which contains water and has a thickness of about 10 .mu.m. (b) In order to observe a moving organism, the exposure time is several .mu. seconds, and a pulse X-ray source and an image formation type of optical system are employed. (c) In order to observe a sample with producing minimum radiation damage, a phase ZP, which can maintain high resolving power of about 20 to 50 nm and high efficiency, is used as the objective optical system, and the X-rays are monochromatized by using a condenser optical system comprising a concave reflecting mirror which is a multilayer film mirror. This permits the photon counting imaging. (d) A two dimensional X-ray imaging element is used for real time observation, and the sample is observed by an optical microscope, which generally produces little damage to the sample, and, if required, the sample is observed by an X-ray microscope. Since X rays significantly damage organisms and easily exceeds the lethal dose, it is necessary to design the X-ray microscope so that a required image can be obtained with the minimum dose. The present invention configured as described above therefore employs an imaging method which uses a photon counting method. In order to dynamically observe an organism by using this photon counting imaging method with producing the minimum damage, the minimum X-ray dose, the detection limit contrast, the detection limit protein thickness, the gradation of the X-ray image formed, the dosage (the absorbed X-ray dose per unit mass), the pulse width, and the spectral width are optimized in view of the following matter: (i) Detection Limit and Dose Amount of Photon Counting Imaging FIG. 2 is a drawing which shows a state of two-dimensional photon counting. In the drawing, the surface of the sample is divided into small regions formed by the resolving power .delta. and the focal depth 2D.sub.f, each of the regions corresponding to one pixel of the imaging element. An image is formed by differences between the numbers of the photons passing through the respective pixels. The number of the photons incident on each of the pixels is n.sub.0, and the numbers of the photons passing through the pixels are various values depending upon the transmittance. It is assumed that the detection of the X-ray photons in the adjacent pixels defined by the resolving power is an independent probability phenomenon and that the X-ray photons obey a Poisson distribution. (The influence of MTF, flare and ghost in the optical system is excluded.) It is also assumed that contrast is mainly formed by differences in absorption, and that the X-rays, which are lost to the outside of the imaging optical system by diffraction scattering, are negligible. (A dark field illumination method utilizing only diffraction scattering X-rays for forming an image is excluded.) If the average of the difference in number of the photons of the adjacent pixels is greater than the dispersion to some extent, it is possible to detect an image. If the number of the photons applied is n.sub.0 [photon number/pixel], therefore, the following equation is established between the average value E and the dispersion of the photons detected in pixels p.sub.1 and p.sub.2 and the detection limit SN ratio (S/N).sub.d. ##EQU1## If the transmittance is T, the average is the following: EQU E(p.sub.1)=T.sub.1 EQU E(P.sub.2)=T.sub.2, and the dispersion in a Poisson distribution is the following: EQU V(P.sub.1)=T.sub.1 EQU V(P.sub.2)=T.sub.2 Since the number n.sub.1 of the X-ray photons detected is n.sub.1 =T .multidot.n.sub.0, as shown in FIG. 2, n.sub.1 and n.sub.2 are the following: EQU n.sub.1 =T.sub.1 .multidot.n.sub.0 EQU n.sub.2 =T.sub.2 .multidot.n.sub.0 The contrast C is defined by the following equation: ##EQU2## From the equations (1) and (2), the following equation is obtained: EQU C.sup.2 (n.sub.1 +n.sub.2).gtoreq.(S/N).sub.d.sup.2 However, when the detection limit contrast C.sub.d &lt;&lt;1, the maximum number of the photons detected is expressed by the following equation: EQU n.sub.max .perspectiveto.(n.sub.1 +n.sub.2)/2 The detection limit contrast C.sub.d is therefore expressed by the following equation: ##EQU3## Although the gradation from zero to the maximum photon number is generally obtained, the reproduced gradation number d.sub.r, which allows the formation of an image with reliability, is the following: ##EQU4## The SN ratio at the detection limit of X-ray photons depends upon the detection method used, the type of the detector used and the like. If it is assumed that an image can be expressed with gradation by using as significant information the photon number n, which is divided by n.+-..DELTA.n/2 (wherein .DELTA.n=2.sqroot.n(.+-..sigma.: standard deviation)), the photon number at the discrimination limit is expressed by the following equation: ##EQU5## When n.sub.max &gt;&gt;.sqroot.n.sub.max &gt;&gt;1, the SN ratio at the detection limit of the X-ray photons is expressed by the following equation: ##EQU6## If the photon number is considered as significant information for each .DELTA.n=4.sqroot.n(+2.sigma.), the following equations are obtained: ##EQU7## When n.sub.max &gt;&gt;.sqroot.n.sub.max &gt;&gt;1, the SN ratio at the detection limit of the X-ray photons is expressed by the following equation: EQU (S/N).sub.d .perspectiveto.2.sqroot.2 If .DELTA.n=6.sqroot.n(+3.sigma.), the following equations are obtained: ##EQU8## Typical photon numbers for gradation are n=0, 1, 4, 9, . . . in a case of (S/N).sub.d .apprxeq..sqroot.2, n=0, 4, 16, 36, . . . in a case of (S/N).sub.d .perspectiveto.2.sqroot.2 and n=0, 9, 36, 81, . . . in a case of (S/N).sub.d .perspectiveto.3.sqroot.2. If the thickness of the sample is t, the thickness of protein is t.sub.p, and the linear absorption coefficients of water W and protein P are A.sub.w and A.sub.p, as shown in FIG. 3, the X-ray transmittance of water T.sub.W is expressed by the following equation: EQU T.sub.W =exp (-A.sub.W .multidot.t) (6) The X-ray transmittance T.sub.s of the sample is thus expressed by the following equation: EQU T.sub.S =T.sub.W .multidot.exp{-(A.sub.P -A.sub.W).multidot.T.sub.p }(7) Since A.sub.P &gt;A.sub.W within the wavelength region (2.3 to 4.4 nm) of the water window, the maximum transmittance T.sub.smax of the sample is expressed by the following equation: EQU T.sub.smax =T.sub.W The photon number at the maximum transmittance is the maximum number n.sub.max of the photons detected. From the equation (2) and the equations, T.sub.1 =T.sub.W and T.sub.2 =T.sub.S, the thickness t.sub.pd of the protein P at the detection limit within the focal depth is expressed by the following equation: ##EQU9## The damage to the organism produced by X-ray irradiation is determined by the dose amount. (The dose amount is the X-ray absorbed dose per unit mass.) If the average transmittance T.sub.sm of the sample is .intg.T.sub.s dS/.intg.dS, the density is .rho., the resolving power of the microscope is .delta., the transmittance of the window of the sample container is T.sub.c, and the objective efficiency is .eta..sub.0, the average absorption factor is (1-T.sub.sm) and the irradiated photon number is the following: EQU n.sub.0 =n.sub.max /(T.sub.w .multidot.T.sub.c .multidot..eta..sub.0) From the photon energy h.gamma. and the mass .rho..multidot..delta..sup.2 .multidot.t, the dosage D.sub.m (.delta.) is expressed by the following equation: ##EQU10## According to the above-described equations, if the maximum number n.sub.max of the photons detected per pixel is known, the detection limit contrast C.sub.d and the reproduced gradation number d.sub.r are determined. If the coefficient of linear absorption A.sub.p, A.sub.w are determined from the wavelength of X-rays, the thickness t.sub.pd of protein at the detection limit is determined. Further, from the average transmittance T.sub.sm of the sample, the transmittance T.sub.c of the window of the sample container, the transmittance T.sub.w of water, the efficiency .eta..sub.o of an object, the density .rho. of the sample, the thickness t of the sample and the resolving power .delta. of the object, the dosage D.sub.m (.delta.) is determined in accordance with the equation (9). Namely, in the photon counting imaging method of the present invention, if the maximum number n.sub.max of the photons detected is known, main performance, i.e., the detection limit (contrast and gradation) and the dosage are determined. (ii) X-Ray Microscopic Imaging with Minimum Exposure In the present invention, on the basis of the above-described results of principal analysis, the minimum X-ray exposure optimum for the photon counting imaging method is determined in accordance with the following method: It is suitable for practical use in view of the examples described below that the maximum number of the photons detected is within the following range: EQU 25.ltoreq.n.sub.max &lt;200 In accordance with this, the minimum exposure is set so that the maximum number of the photons detected per pixel is within the above range. The above-described maximum number of the photons detected is determined on the basis of the investigation below. The prerequisites are the following: (1) The wavelength used is about 2.5 nm within the wavelength range (2.3 to 4.4 nm) of the water window which exhibits good transmittance of water and which permits the contrast of an organism to be easily obtained. (2) The linear absorption coefficients of water and protein at the wavelength are the following: EQU A.sub.w =0.13/.mu.m EQU A.sub.p =1.5/.mu.m (3) The thickness t of the sample is 10 .mu.m, which allows the observation of one cell, in consideration of the balance between the transmittance of water and the thickness of the cell. (4) The average transmittance T.sub.sm is determined on the assumption that the average thickness of cell protein is expressed by the following equation: EQU T.sub.pm =0.15.multidot.t (5) The density .rho. of the sample is about 1 g/cm.sup.3. (6) The transmittance of the window of the sample container is T.sub.c =0.63, and the efficiency of the object is .eta..sub.o =0.3. These values are described in detail below. If the maximum photon number n.sub.max is determined on the above-described assumption, the following results are obtained: (a) In a case of n.sub.max =100 ##EQU11## In this case, when the resolving power .delta. is 20 nm, the dosage exceeds the lethal dose (.perspectiveto.1.times.10.sup.4 J/Kg). (b) When n.sub.max is 200 or more, although it is possible to observe a sample with lower contrast than that in the case (a), there are the following problems; (A) The dosage is increased and exceeds the lethal dose of cells. (B) Since the X-rays must be further monochromatized for maintaining the precision of photon detection, a spectral element other than the multilayer film mirror and the like is required (described below). (C) Since the coefficient of utilization of the X-ray source is decreased owing to a decrease in the spectral width, a large strong X-ray source is required. (c) When n.sub.max is 25 or less, even if the resolving power is 20 nm, although the dosage is reduced to a level below the lethal dose, the detection contrast C.sub.d is 0.2 or more, the reproduced gradation number d.sub.r is 5 or less, and the limit protein thickness is 300 nm or more. The restrictions on the image quality and the sample detection are thus increased, resulting in a problem in practical use. (d) Evaluation of performance and sample treatment A) When the thickness t.sub.p of protein is smaller than the detection limit thickness t.sub.pd, as in (B) of the case (a), since the contrast C.sub.d of the organism sample can be increased to a level higher than about 0.1 by vital staining (VS) of the organism with gold having a thickness of t.sub.gd =8.4 nm, the organism can be easily observed. The thickness t.sub.gd of gold used for vital staining VS is determined by substituting the linear absorption coefficient A.sub.g =24/.mu.m [.lambda.=2.5 nm] into the equation (8) in place of A.sub.p. B) In this way, vital staining is necessary for observation of a low-contrast thin sample such as intracellular minute organs, virus and the like. The X-ray exposure can be decreased by vital staining of a specific part so as to significantly improve the contrast of a sample. For example, although the maximum photon number n.sub.max of 100 is required for observing a sample having contrast C of 0.1, the contrast C is improved to 0.2 by vital staining of the sample with gold having a thickness t.sub.gd of 8.4 nm. It is therefore found from the equation (3) that the stained sample can be detected with the maximum number n.sub.max of the photons detected of 25. Namely, the exposure is decreased to 1/4, and the dosage is thus decreased to 1/4. C) Although the dosage exceeds the lethal dose of 1.times.10.sup.4 J/Kg when the resolving power .delta. is 20 nm, as in (C) of the case (a), in such a case, it is effective to perform treatment such as cooling of an organism sample for the purpose of decreasing damage to the sample and retarding the metabolism of the cells. (iii) Detection limit when flare is present When a zone plate is used as an image forming element, although the first diffracted light is used as image forming light, flare is generated by the other orders of diffracted light. The possible influence of the flare is the following: Flare generally uniformly spreads over the surface of the image formed and is thus considered as fuziness of the diaphragm or the sample, which is caused by the optical system. The intensity of flare therefore depends upon the intensity of irradiation, the average transmittance of the sample and the size of visual field (the diameter of the real visual field). If the flare coefficient is .eta..sub.f (which can be calculated, as described below) of the optical system, the flare photon number n.sub.f and the detected photon number n.sub.I are expressed by the following equations: EQU n.sub.f .perspectiveto..eta..sub.o .multidot..eta..sub.f .multidot.T.sub.sm .multidot.n.sub.o ( 10) EQU n.sub.I .perspectiveto..eta..sub.o (T.sub.s +.eta..sub.f .multidot.T.sub.sm)n.sub.o ( 11) From the equation (11), the number of the photons detected in each of the pixels is expressed by the following equations: EQU n.sub.1 .perspectiveto..eta..sub.o (T.sub.1 +.eta..sub.f .multidot.T.sub.sm)n.sub.o EQU n.sub.2 .perspectiveto..eta..sub.o (T.sub.2 +.eta..sub.f .multidot.T.sub.sm)n.sub.o The maximum number of the photons detected is thus expressed by the following equation: EQU n.sub.max .perspectiveto..eta..sub.o (T.sub.max +.eta..sub.f .multidot.T.sub.sm)n.sub.o When flare is present, the contrast C.sub.I of a detectable image and the contrast C.sub.s of a desired sample must be discriminated. The contrast is defined by the following equations: EQU C.sub.I .ident..vertline.n.sub.1 -n.sub.2 .vertline./(n.sub.1 +n.sub.2)(12) EQU C.sub.s .ident..vertline.T.sub.1 -T.sub.2 .vertline./(T.sub.1 +T.sub.2)(13) From the above-described relation between n.sub.1, n.sub.2 and T.sub.1, T.sub.2, the following equation is established: EQU C.sub.s =C.sub.I (n.sub.1 +n.sub.2)/(n.sub.1 +n.sub.2 -2n.sub.f)(14) As described in (i), the contrast D.sub.I of the image and the detection limit SN ratio has the following relation: EQU C.sub.I.sup.2 (n.sub.1 +n.sub.2).gtoreq.(S/N).sub.d.sup.2 ( 15) From the above equations (14) and (15) and the following equation: EQU n.sub.max .perspectiveto.(n.sub.1 +n.sub.2)/2, the detection limit contrast C.sub.sd of the sample, the reproduced gradation number d.sub.sd and the detection limit protein thickness t.sub.pd are expressed by the following equations: ##EQU12## Although the performance is therefore deteriorated by the presence of flare, the detection limit can be evaluated and calculated by the above equations. (iv) Pulse Width Required for Dynamic Observation If the resolving power is .delta., and the velocity is v, it is necessary that the exposure time t.sub.x required for obtaining a clear image of a moving object without having blurring or deformation has the following relation: EQU t.sub.x .ltoreq..delta./(10.multidot.v) (19) Since the present invention aims at an X-ray microscope having resolving power .delta. of about 10 nm, and the maximum value V.sub.max of the velocity of plasma streaming an the ciliary and flagellous movements is expressed by the following equation: V.sub.max .perspectiveto.1 mm/s, the exposure time t.sub.x is the following: EQU t.sub.x .perspectiveto.1 .mu.s Since exposure for a time of as short as 1 .mu.s cannot be easily realized by using the scanning type of apparatus, it is rational to use a image-formation microscopic system which uses a pulse X-ray source. A system of exposure for a time of as short as 1 .mu.s is useful for observing the thermal motion of the sample and the vibration of the apparatus, and thus permits the formation of a small vibration isolator. (v) Maximum Number of Detected Photons and Spectral Width in Photon Counting As described above, in order to dynamically observe a living organism, a conventional photon counting method in time series is not used, and it is necessary to count the photons over all the pixels for a moment of about 1 .mu.s. In order to prevent error from occurring in counting of photons, since the energy difference caused by the wavelength difference must be less than the energy of one photon, the following equation is established: EQU .DELTA.n.multidot.h.multidot..gamma.&gt;n.sub.max .multidot.h.multidot..DELTA..gamma. Since the following equations are established: EQU .DELTA.n=1, .gamma.=c/.lambda. and .gamma./.DELTA..gamma.=.lambda./.DELTA..lambda., the maximum detected photon number n.sub.max has the following relation: EQU n.sub.max &lt;.lambda./.DELTA..lambda. (20) As described above, it is preferable that the maximum number of the detected photons is within the following range: EQU 25.ltoreq.n.sub.max &lt;200 The spectral width .DELTA..lambda. and the number of periods N.sub.c of the multilayer film of the multilayer film mirror which defines the spectral width have the following relation: EQU .lambda./.DELTA..lambda..perspectiveto.N.sub.c ( 21) If 50&lt;N.sub.c &lt;400, therefore, the conditions for monochromatizing the X-rays are satisfied. If the number of periods Nc of the multilayer film is about 400 or less, it is possible to observe a sample having a lower degree of contrast. For example, it is possible to observe a sample having contrast which is 1/2 of that in a case of Nc of 100. However, since the dosage of the organism is increased 4 times, the damage of the organism is increased, and the organism frequently dies after the observation. In addition, since an attempt can be made to further monochromatize the X-rays by increasing the number of periods, the restrictions on the chromatic aberration of the objective optical system are decreased, and an attempt can be thus made to improve the performance by, for example, enlarging the effective visual field. However, in combination of usual materials, the reflectivity is not improved in proportion to an increase in number of the layers. In addition, an increase in number of the layers causes a deterioration in the efficiency of utilization of X-rays and causes the need for a stronger X-ray source and an increase in size of the whole apparatus. The number of periods is thus limited to about 400, and the further monochromatization of X-rays is unsuitable for practical use from the viewpoint of a reduction in size of the X-ray source and damage to the organism. On the other hand, when the number of periods Nc of the multilayer film is less than 50, it is possible to decrease the number of irradiated photons during photon counting and decrease the damage to the organism. However, the X-rays cannot be easily monochromatized, the chromatic aberration of the objective optical system is made remarkable, and the counting error in photon counting is increased. This creates a deterioration in detection performance and a problem in practical use because only a sample having high contrast can be observed. In addition, when the number of periods is small, it is difficult to achieve sufficient reflectivity within the X-ray region in the multilayer film mirror. (vi) Sensitivity of Two-Dimensional X-Ray Imaging Element A single photon can be detected with ideal highest sensitivity. Since the average number of the electron hole pairs generated, which serve as signals, is greater than the number of noise electrons in dark when the incident X-ray photon is one within the soft X-ray region, high sensitivity can be realized if the quantum efficiency and the vignetting factor are close to 100%. In a case of a solid state image sensor, if the wavelength of the X-rays used is .lambda.=2.5 nm, and the photodetector element is Si, the average number n.sub.p of the electron-hole pairs generated is 137, the standard deviation .sqroot.n.sub.p F is 4, the Fano factor F is 0.12 and the number of noise electrons in dark is 50 (electrons/pixel). The number of noise electrons in dark can be reduced to about 10 (electron/pixel) by cooling.