GB1558405A

GB1558405A - Tomography

Info

Publication number: GB1558405A
Application number: GB23228/76A
Authority: GB
Original assignee: University Patents Inc
Current assignee: University Patents Inc
Priority date: 1975-06-16
Filing date: 1976-06-04
Publication date: 1980-01-03
Also published as: FR2315090A1; DE2627084A1; NL7606543A; SE7606779L; JPS5220789A

Description

(54) TOMOGRAPHY (71) We UNIVERSITY PATENTS INC., a United States Corporation organized under the laws of the State of Delaware, of 2777, Summer Street, Stamford Connecticut 06905, United States of America, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement:- This invention relates to apparatus for generating a two-dimensional back-projected image of a slice of an object and may be applied to imaging cross-sections of objects using transverse X-ray tomography techniques.

Using conventional X-ray imaging techniques, a shadow view of a body under examination can be produced, but it does not contain information concerning the depth of details in the body. In many cases it is not possible to distinguish small objects since they are obscured by the structures of larger objects; e.g., bones. This drawback has been overcome to some degree by the development of body-section radiography techniques luiown as X-ray tomography.

Radiographic transverse tomography attempts to view sections or "slices" which are perpendicular to the axis of a patient. In a "classical" transverse tomographic system, incident X-radiation is passed through an object being studied at an angle and is imaged on a film. In order to image a particular slice, both the film and the object are rotated synchronously during the X-ray exposure.

Shadows of points in a single plane of the object are continually projected on to the same place on the film during the rotation, whereas shadows of other parts of the object move in relation to the film. Thus, while the slice of interest is imaged relatively sharply, the resultant picture is overlaid by the motionblurred images of other parts of the object.

As a consequence, the resultant "tomogram" tends to lack contrast and fine detail is obscured.

Recently, digital processing techniques have been applied to the tomographic imaging problem and a degree of success has been achieved whereby blurred images of overlying and underlying planes have been removed so as to permit detection of greater detail. However, digital methods require the processing of extremely large quantities of data, and even fast computers take significantly long times to do the necessary computations.

Accordingly, commercial computer tomography equipment is extremely expensive and beyond the financial reach of many who desire it.

In another type of transaxial tomography, a narrow beam of X-rays is employed and only the rays passing through the desired cross-section are incident on a film so, ideally, only information about the particular slice is recorded. The result is a so-called "one-dimensional projection". A plurality of one-dimensional projections can be obtained by passing X-rays through the same cross-section at a number of different rotational angles. The resultant set of one-dimensional projections can be processed optically. Alternatively, the values of each projection can be fed to a computer for digital analysis, whereby the density function of each elemental area in the plane is computed by one of a number of mathematical techniques which utilize iteration, mathematical filtering techniques, and other known solutions.

An early technique for optical processing of a set of one-dimensional projections is disclosed in U.S. Patent No. 2,281,931 wherein a cylindrical lens system is utilized to optically "enlarge" each one-dimensional projection in a direction perpendicular to the plane of the section. Each enlarged one-dimensional projection is a two-dimensional image and the set of two-dimensional images which result from optically enlarging each one-dimensional projection are superposed with mutual angular displacements that correspond to the rotation angles at which the one-dimensional projections were originally taken. The image ultimately produced in this manner has been referred to as a "layergram" of the cross-section. In recent years, attempts have been made to process the layergram using spatial filtering methods of both optical and digital natures to restore the layergram image which is known to suffer blurring. However, the digital processing techniques again involve the handling and lengthy processing of large amounts of data, which is very expensive. Optical processing techniques toward this same end have generally been found to be either inadequate from a performance standpoint or unduly complex and expensive.

The technique described in the abovereferenced U.S. Patent No. 2,281,931 is one of a number of image-reconstruction techniques which utilize the "back-projection" of an image. Generally, the term "back-projection" implies that the value of a particular point in a projection is assigned to all points on a line perpendicular to the projection. The values of overlapping lines are integrated for all projections. The result is equivalent to back-projecting the values in each one-dimensional projection through the object and integrating their overall effect. As implied above, a simple back-projection yields results which are generally considered inadequate, and it is presently believed that a technique of back-projection combined with a suitable filtering technique, could yield quality results.

However, as emphasised above, such techniques have in the past required expensive and complex systems.

Apparatus according to the invention comprises an image carrier having a plurality of substantially parallel elongate optical images thereon, each elongate image having an optical characteristic varying along its length in accordance with the one-dimensional density characteristic (as herein defined) of the said slice of the object obtained at a particular relative rotational angle of the object about a predetermined axis perpendicular to the slice; photodetector means; means whereby the photodetector means responds to a changing portion of the image carrier, the said portion being substantially a sinusoid whose axis is perpendicular to the said elongate optical images; and display or recording means responsive to the output of the photodetector means for displaying or recording the backprojected image.

The "one-dimensional density characteristic" is the linear density variation obtained by projection in a given direction through the slice and in the plane of the slice. The optical characteristic of the elongate images may be transmissivity or reflectivity.

In a preferred embodiment of the invention the carrier means is a cylindrical film having elongate images thereon with transmissivities that represent the one-dimensional density characteristic of the slice of the object under consideration, the elongate images extending parallel to the axis of the cylindrical film.

In this embodiment, means are provided for uniformly illuminating the projections and optical means, including masking means, are provided in spaced relation to the cylindrical film and are operative to image a sinusoidal portion of the cylindrical film onto the photodetector means. Means are provided for rotating the cylindrical film on its axis so that different groups of elongate images on the film contribute to the said sinusoidal portion of the carrier to which the photodetector means responds. Means are also provided for tilting the axis of the cylindrical film, whereby the said sinusoidal portion of the cylindrical film is of varying amplitude. In this embodiment the display means is synchronised with the rotational rate of the cylindrical film and with the tilting rate of the axis of the cylindrical film, so that the displayed or recorded elements corresponding to successive outputs of the photodetector means together constitute the required image of the slice.

In accordance with another advantageous embodiment of the invention there is provided a photodetector and illuminating means directed toward the photodetector. The image carrier is placed in the light path between the illuminating means and the photodetector. A mask, also disposed in the said light path, comprises a transparent track including a plurality of cycles of substantially sinusoidal form and of varying sinusoidal amplitude.

Means are provided for moving the carrier and the mask with respect to each other.

Finally, a display or recording means, syn chronised with the moving means, is respon sive to the output of the photodetector for displaying the back-projected image. In one form of this embodiment of the invention the mask comprises a movable endless loop and the amplitude of the substantially sinusoidal transparent track varies between zero and a predetermined maximum. In this embodiment the mask has an optical characteristic trans verse the length thereof which corresponds to a predetermined filter function so that a fil tered back-projection is obtained.

In the preferred form of apparatus using a cylindrical carrier the means whereby the photodetector means responds to a portion of the image carrier of sinusoidal form comprises an optical filter mask having an optical trans mission characteristic representing a filter function effective to compensate, at least partially, for blurring in the said optical characteristic along the said sinusoidal portion.

In order that the invention may be better understood, some examples of apparatus and methods embodying the invention will now be described with reference to Figures 3 16 of the accompanying drawings (Figures 1 and 2 illustrating known techniques). In the drawings: FIG. 1 is a diagrammatic representation of a technique for generating one-dimensional projections of a slice of an object; FIG. 2 shows another technique for obtaining one-dimensional projections of a slice of an object; FIG. 3 is a diagram of a slice of an object useful in understanding approaches to obtaining the density characteristic of said slice; FIG. 4 shows graphs useful in describing the convolution of a filter function with a one-dimensional projection; FIG. 5 is an elevational perspective view, partially in schematic block diagram form, of an apparatus in accordance with an embodiment of the invention; FIG. 6 is a representation of a slice of an object, along with explanatory graphs, which are useful in understanding the invention; FIG. 7 is an elevational perspective view, partially in schematic block diagram form, of an apparatus in accordance with another embodiment of the invention; FIG. 8 is a simplified perspective representation of a portion of the invention which is useful in facilitating understanding the embodiment of FIG. 7; FIG. 9 is a simplified perspective representation of a portion of the invention which is useful in facilitating understanding of the embodiment of FIG. 5; FIG. 10 is another simplified perspective representation of a portion of the invention which is useful in facilitating understanding the embodiment of FIG. 5; FIG. 11 shows the nature of the optical masks utilized in the embodiment of FIG. 5; FIG. 12 is another simplified perspective representation of a portion of the invention which is useful in facilitating understanding of the embodiment of FIG. 5; FIG. 13 illustrates a portion of the mask means in accordance with the embodiment of FIG. 7; FIG. 14 illustrates a portion of another mask means in accordance with the embodiment of FIG. 7; FIG. 15A illustrates a portion of another mask means in accordance with an embodiment of the invention and FIG. 15B shows a modification of FIG. 7 for use in conjunction with the mask of FIG. 15A; FIG. 16 is a schematic representation illustrating a technique for generating the mask means of FIG. 7.

FIG. 1 illustrates the nature of one-dimensional projections of a body cross-section or slice which can be obtained, for example, in accordance with a technique set forth in the above-referenced U.S. Patent 2,281,931. A body 20, of which a cross-section 21 is to be reproduced, consists of an annular portion 23 of semi-transparent material, such as muscle tissue of a human limb, and a core portion 24 of a material which is less transparent to X-rays, such as bone. A beam of parallel Xrays 30 emanating from a remote source (not shown) passes through body 20, and a narrow portion of the X-ray beam, having a bandshaped cross-section, passes through a narrow elongated slot 41 in a diaphragm 40, which is typically formed of lead. The X-ray beam passing through slot 41 produces a narrow elongated image 51 on X-ray sensitive film member 50, which is provided in the shape of a cylinder. The image 51 can be considered as a one-dimensional projection whose optical characteristic corresponds to the different degrees of absorption of the X-rays by the portions 23 and 24 of the body 20 at section 21.

The elongated strip 51A at the right of FIG. 1 illustrates a simplified version of the one-dimensional projection 51 which is recorded on film 50, but in "positive" form. It is seen that the central portion of the projection is darkest due to the low transmissivity of core 24 to X-rays and the resultant lesser exposure of the corresponding portion on film 50. (It should be noted that since the thickness of annular portion 23 increases toward the center, the overall transmissivity of this part will also decrease gradually toward the center of body 20 but, for ease of explanation, this gradation is not shown in the simplified illustration of strip 51A or the curve 51B which follows.) The curve 51B illustrates graphically the one-dimensional density characteristic of the slice 21 for the direction indicated, i.e. the density function of the slice 21 as a function of length along slot 41, this length being indicated by the coordinate "x".

The density, indicated as fi (x), is seen to correspond to the relative transmissivity of the cross-section as a function of x; i.e., the inverse of the density characteristic.

Returning to the structural portion of FIG.

1, the body 20, and consequently also the section 21 thereof, are rotated about an axis 27 which is normal to the plane of section 21 at the point of rotation, the rotation being represented by curved arrow 28. The cylindrical film 50, which is typically mounted on a drum, is rotated on its axis in angular synchronism with the rotation of body 20. At each of a number of discrete rotational positions, the body and the film 50 are stopped and a one-dimensional projection is recorded (like strip 51A). Accordingly, after a full 3600 of rotation the cylindrical film 50 will contain a "set" of one-dimensional projections, i.e., the various fi (x), each one-dimensional projection having an optical characteristic which represents the density characteristic of the section or slice 21 of the object 20 as measured at a particular relative rotational angle.

Referring to FIG. 2, there is shown another known technique of obtaining one-dimensional projections of a slice or section 61 of a threedimensional body 60. A collimated "pencil" beam of X-rays is generated by a source 62, passed through the section 61, and received by a small-area sdntillation detector 63, the output of which is indicated by a point on the graph at the right of FIG. 2. The source 62 and detector 63 are moved synchronously across the slice 61 and an output data value is obtained at each spaced position, each data point representing the intensity of the transmitted X-ray beam. The resultant function ft (x) is a one-dimensional projection similar in information content to those obtained using the system of FIG. 1, and as designated by the graph 51B of FIG. 1. It will be appreciated that, if desired, one could obtain an optical characteristic such as that of projection 51A from the data of FIG. 2 by utilizing the output of the detector 63 to modulate the intensity of a scanning beam exposing a film strip. More typically, the data points obtained from detector 63 are processed using a digital computer. A "set" of one-dimensional projections, fi (x), are obtained by taking the depicted measurements at a number of different rotational angles of the section 61, and the totality of the data is processed by a computer to attempt reconstruction of the elemental density function of the two-dimensional slice 61 of object 60. A problem of the system of FIG. 2 arises in maintaining registration and collimation when stepping the source and detector to different positions. An alternative technique employs a plurality of sources and/or detectors, but this requires precise balance of the multiple components as well as additional switching circuitry.

FIG. 3 is helpful in further illustrating the nature of the obtained one-dimensional projections, as well as in understanding approaches to obtaining the density characteristics of a section or slice of an object from such projections, and especially approaches which utilize "back-projection". A thin section or slice 90 under investigation is depicted as being rectangular for ease of explanation. The section is divided into an array of small elemental units which comprise an m by n array wherein each element is designated by its position in the array and assumed to have a density which is to be ultimately determined.

Thus, for example, the density of the element in the upper left hand corner is designated by dull, its adjacent neighbor to the right has a density designated by dl2, and so on. The beam, or portion of the beam (e.g. in FIG.

2 or FIG. 1), passing through a particular row of elements is designated by I with two subscripts, the first subscript indicating the reference angle at which the X-ray energy is passed through the slice 90 (a 00 reference angle is shown in FIG. 3, so the first subscript is 0), and the second subscript indicating the relative position of the particular beam or beam portion along the one-dimensional data coordinate (e.g. the x axis in FIGS. 1 and 2). The detected beams, or portions thereof, which have passed through the slice 90 are designated by primed versions of the input beams. Each output is equal to its corresponding input times a function of the elemental densities through which the beam or beam portion has passed. For example, it is seen that 1C1 is equal to Io1 times a function of the elemental densities of the first row of the array, as shown. Similarly, the remaining outputs are each also functions of the elemental densities in their corresponding rows. It will be appreciated that in the expressions for the one-dimensional projection values for a particular reference rotational angle (0 for the illustrated case), there are many more unknowns than equations. However, if the slice is now rotated on its axis to a number of different positions, and additional one-dimensional projection data values are obtained at each rotational angle, the full "set" of one-dimensional projections will yield a large number of equations which can be used to determine the unknowns; i.e., the individual elemental densities in the slice 90.

As referred to in the introductory portion of the Specification, the set of one-dimensional projections can be processed by computer using various techniques. One type of prior art solution uses an iterative technique wherein assumed elemental density values are assigned to each member of the array. The computer calculates the output intensity values that would be obtained from the model, and these calculated output intensities are compared with the actual output intensities to obtain error values. The error values are examined and used to calculate appropriate modifications of the model which will yield smaller error values, and the process is continued until a model is obtained which yields error values that are considered acceptably small. Depending on the particular algorithm used, it will take at least some minimum number of computations for the model to "converge" to an acceptable state.

In any event, the computer must have adequate speed, memory, etc. to obtain a solution within a reasonable time, so the equipment needed can be prohibitively expensive. A number of techniques have also been attempted wherein the computer systematically solves the simultaneous equations by classical means or employment of known matrix manipulation methods. Unfortunately, these approaches are also found to require very large numbers of calculations and expensive computer equipment is needed for solution within practical time constraints.

In the "back projection" image reconstruction technique treated above, the value of a particular data point in a projection is assigned to all points on a line perpendicular to the projection. In terms of FIG. 3, for example, the value Iol' would be assigned to each of the elements in the row to which that output intensity is attributed; viz., dull, d12 ... dim.

Similarly the output intensity value Iso,' is applied to all of the elemental densities in the second row; viz., d21, d22, . . . d2m, and so on for the remaining rows. Next, the output data values of the next one-dimensional projection are assigned in the same manner to each elemental density, and this is done for each relative rotation angle at which a onedimensional projection was obtained. Thus, at the completion of the back-projection, each elemental density has a final value which equals the sum of all the data values attributable to it during the process previously described. The back-projection process can be performed either on a digital computer or optically, but the results of a simple backprojection have been found inadequate in most cases due to blurring.

In order to derive better results using backprojection techniques, it has been suggested that a technique of "filtering" be used in conjunction with back-projection. The filtering can be thought of as a type of selective "weighting" which aids in restoration of a true density characteristic by removing blurring effects. The filtering can either be done on the one-dimensional projections before the back-projection operation, or it can be done on the reconstructed back-projected image. FIG. 4 illustrates the filtering of a particular one-dimensional projection designated fi (x) using a filter function designated by h (x). Mathematically, the two functions fi (x) and h (x) are convolved to obtain the resultant filtered one-dimensional projection which is designated g, (x). The convolution operation can be visualized graphically by considering the filter function h (x) as being moved along the x axis and a multiplcation between fi (x) and h (x) being performed at each point of the excursion of the filter function. For example, in FIG. 4 the filter function is shown at an abscissa position s and the resultant anta pomt on the function g1 (x) (as shown by the dot on the third graph) is obtained by multiplying h (x) at this position by the function fi (x). This operation is performed at each point along the x axis and the function g1 (x) is obtained in this manner. As disclosed in a publication of Cho et al in IEEE Transactions on Nuclear Science, Vol. NS-21, page 44 (June, 1974), one-dimensional projections are convolved with a processing function, as just described, the operation being performed on a digital computer.

The type of filtering and back-projection techniques just described, as well as those where convolution is performed after backprojection, involve large numbers of computations when performed on a digital computer, so expensive computing capability is required.

Optical techniques have been attempted for performing these operations. For example, it is known that lenses perform Fourier transformation when coherent light is used. However, such systems tend to be limited by such factors as necessary photoreductions and film thickness variations.

Referring to FIG. 5, there is shown an embodiment of an apparatus 100 in accordance with the invention. A cylindrical drum 101, which may be formed of a suitable translucent material, such as a white plastic, is provided at its top and bottom ends with support ribs 102. Axially disposed members 103 are secured to the support ribs and protrude beyond the ends of drum 101. An elongated light source 104, which may comprise a long thin incandescent source (energized by means not shown) is mounted between the support ribs 102 along the axis of the drum. The light source provides substantially uniform illumination of the surface of the drum. The plastic surface of drum 101 acts as a light diffuser to ensure the uniform illumination.

The upper axial member 103 is coupled to a small electric motor 105 which is, in turn, mounted on a bracket 106. The motor 105 is energized by a signal on a line 150A and causes relatively fast rotation of axial member 103 and, in turn, rotation of the drum 101 on its axis, as indicated by arrow 112. Upper and lower circular support members 107 and 108 are provided with central elongated slots 107A and 108A, respectively. The slot 107A receives a bearing of the bracket 106 and acts to guide the motion of the bracket and the slot 108A receives and retains an end bearing 109 therein. Mounted within bracket 106 is an additional electrical motor means (not visible) which is energized by a signal on line 150B. The motor within bracket 106 drives gearing which meshes with teeth 110 formed along the edge of the circular support member 107, and the motion of the gearing causes relatively slow movement of the bracket 106 which follows a path in one direction along the support 107 and then returns along the other direction in reciprocating fashion and as indicated by two-headed arrow 111. Accordingly, it is seen that the drum 101 spins at a relatively fast rate and tilts back and forth about its center at a relatively slow rate.

Mounted on the drum 101 is a film 120 which has recorded thereon a plurality of substantially parallel elongated projection images, each projection image having a transmissivity which represents the density characteristic of a cross-section or slice of an object as measured at a particular relative rotational angle. The film 120 may be recorded in the manner described in Figure 1, or by using variations on the technique described in conjunction with Figure 2. Each projection is of the general type described with reference to the strip 51A in Figure 1, and the full 360" of arc of the film 120 contains adjacent pro jections taken at rotational increments of the object slice in question as it is rotated a full 3600.

In Figure 5 the drum 101 is shown at an instant when it is in its vertical orientation.

The optical receiving portion of the apparatus of Figure 5 has its optical axis along the horizontal (i.e., perpendicular to the particular orientation of the drum shown in the Figure). A lens 130 is representative of optics which receives and collects light from the film 120 and focuses the light at a pair of foci at which masks 135 and 136 are disposed, a beam splitter 131 effecting the division of the collected beam. The masks 135 and 136 achieve a filtering function of the type described in conjunction with Figure 4, as will be described hereinafter. Large-area photodetectors 137 and 138 receive the light passing through masks 135 and 136, respectively, and generate output signals as a function of the received light intensity.

The photodetectors 137 and 138 view at any instant a line extending around that half of the drum which faces them. If the drum axis is normal to the optical axis of the lens 130 the viewing line is normal to the said axis throughout the rotation of the drum. If the drum is tilted, the viewing line is a halfsinusoid, the amplitude of which is increased as the tilt is increased. The effect of the slow tilt and fast spin of the drum 101 is that at one extreme position of tilt the viewing line is a half-sinusoid of maximum amplitude on the rotating drum, the amplitude decreasing as the tilt is reduced and increasing again as the tilt is increased in the opposite direction; thus the peak sinusoidal amplitude of the viewing line varies with time relative to an axis or base line substantially perpendicular to the parallel optical projections or images on film 120.

The output of photodetector 138 is subtracted from the output of photodetector 137 by difference amplifier 139, whose output is a video signal designated "V". A scanning signal generator 150 generates output voltages on lines 150A and 150B which, it will be recalled, control the rate at which the drum 101 rotates and tilts. These signals also control the deflection circuitry of a display 160 (which could alternatively be a recorder), so as to produce a spiral scan raster which has a radial component that varies in accordance with the signal on line 150B and a rotational component which varies in accordance with the signal through the slit at any given instant. In FIG.

9, only a single one-dimensional projection is depicted, and the point on this particular one-dimensional projection which is "seen" through the slit is indicated by the dark dot.

It can be shown that the displacement of the points (i.e., the point on the one-dimensional projection shown as well as on all other one-dimensional projections seen through the slit) with respect to the slit is given by ax=Rsino sin(+ebi) where R is the radius of the cylindrical drum, suc is the rotational angle of a data point under consideration, d is the tilt angle with respect to the vertical, and 8i is the relative rotational angle at which the one-dimensional projection containing a data point under consideration was taken (again, FIG. 6). Accordingly, by setting B=+e and Rsin=r, the displacement Ax is seen to be equivalent to the required shift in the convolution integral represented by expression (2). In the setup of FIG. 5, the integration operation is carried out by the large-area photodetectors 137 and 138.

The film 120 on FIG. 5 can be initially recorded with a substantially logarithmic transmission characteristic, as follows from the known essentially linear Hurter-Driffeld characteristic of photographic film.

FIG. 10 is intended to give further insight as to the sections on the film which are imaged through a simplified mask, such as the slit used in describing the model of FIG.

9. In FIG. 10 the optical axis is assumed to be perpendicular to the plane of the paper, and the top of the cylinder can be thought of as being tilted into the paper and away from the viewer. The dotted lines show the sections on the cylinder which are "seen" through a slit on the optical axis as the cylinder is tilted to various angles o. The sections of the cylindrical drum which are "seen" are intersections of planes with the tilted cylinder which result in elliptical sections on the cylinder and a corresponding sinusoidal pattern on the film. Only at the =0 position shown in FIG. 5 will the imaged section be a circle.

In all cases, the data points on a particular elliptical section being imaged will correspond to the totality of the back-projected contributions of a particular point P in the slice of the object under consideration (FIG. 6), the point P being defined by r (which was seen above to equal Rosins and oi. In operation of the system of FIG. 5, the cylindrical drum spins rapidly, varying f (as controlled by the signal on line 150A) and therefore tracing out a circle in the reconstructed image. A relatively slower linear scan of sin f (the tilt rate being controlled by the signal on line 150B) varies the radius of the traced out circle, so a spiral is obtained, as is the case where the signals on lines 150A and 150B are utilized to control deflection circuits in display 160 in the manner indicated above.

For purposes of understanding the manner in which the apparatus of FIG. 5 generates a back-projected image, the diagrams of FIGS.

9 and 10 substituted a simple slit for the masks 135 and 136 of FIG. 7, through which the cylindrical drum is actually viewed. FIG.

11 illustrates a type of mask which is suitable for use in the apparatus of FIG. 7. The filter function, h (x), is shown in FIG. 11, is of the type described in conjunction with FIG.

4 and also shown diagrammatically in the explanatory FIG. 6. The masks represent the filter function as a photographic transparency, and since h (x) takes on both positive and negative values, two separate transparencies are utilized to represent a positive and negative parts of h (x). The following equations show how h (x) is represented by the h+ (x) and k (x) mask functions:

h (x) e ro ,F h(x) < 0 + thtx) rf h (x) = r-h(X) If htx790 - IF hC?O h axis h(x)-h(X) , ~ The masks of FIG. 11 utilize binary approximations of the filter function h (x). For example, the relatively large central transparent portion of the h+ (x) mask and the two relatively thin transparent adjacent portions of this mask relate in size to the areas under the positive portions of the h (x) function, whereas the two transparent portions of the h (x) mask are related in size to the area under the negative portions of the h (x) curve. The desired bipolar output is obtained as the output of differential amplifier 139, which generates the difference between the light intensity "seen" through the two masks. From FIG. 6, it can be envisioned how the masks effectively achieve the desired convolution for each point being reconstructed.

FIG. 12 illustrates the sections on cylindrical drum 101 which are "seen" through the h+ (x) mask at a tilted orientation of the cylindrical drum (the "seen" portions being shown shaded). The shaded elliptical sections are seen to correspond in thickness and spacing to the transparencies of the h+ (x) mask.

Thus, it can be visualized how the optical system of FIG. 5 performs the desired filtering and back-projection operations simultaneously by optically selecting appropriate sinusoidal patterns on the film (corresponding to elliptical sections on the cylinder) having transparencies which represent the original onedimensional projections of the object slice being studied.

Referring to FIG. 7, there is shown an apparatus 100 in accordance with another embodiment of the invention. A carrier of film 120 is supported in an opaque frame 121. The film has recorded thereon a plurality of substantially parallel elongated projection images, each projection image having a transmissivity which represents the density characteristic of a cross-section or slice of an object as measured at a particular relative rotational angle.

The film 120 may be recorded in the manner described in conjunction with FIG. 1, or by using variations on the technique described in conjunction with FIG. 2. Each projection is of the general type described with reference to the strip 51A in FIG. 1, and, in the present embodiment, the full 3600 of arc of the film 120 contains adjacent projections taken at rotational increments of the object slice in question as it is rotated a full 3600.

Spaced from the film 120 is a movable mask 140, to be described, which is in the form of an endless film loop mounted on a sprocketed roller 151 and idler rollers 152-154. A lamp 130 illuminates the film 120 and the light passing therethrough and through the mask 140 is incident on a photodetector 150. In the present embodiment lens 172 images the projections on the film 120 onto the mask 140 and lenses 171 and 173 focus the light source for collection at the detector. It will be understood, however, that various alternative optics can be employed.

The sprocketed roller 151 has a sprocket wheel 155 which engages sprocket holes on the edge of the mask film loop 140. A synchronous motor 180 drives the sprocketed roller 151 at a constant speed and a shaft encoder 181 generates an output signal 181A as a function of the roller position. Gearing 182 steps down the rotational rate of the roller 151 at a ratio to be described, and the rotation of gearing 182 is sensed by another shaft encoder 183 which generates an output signal 183A. Signals 181A and 183A synchronize the scan pattern of a display 190 (which could alternatively be a recorder) which also receives the output of the photo detector 150 to modulate the brightness of the display. The resultant displayed or recorded image represents the filtered twodimensional back-projected image of the slice of the object from which the one-dimensional projections on film 120 were originally made.

An understanding of the operation of the apparatus of Figure 7 is facilitated by examining Figures 6 and 8 and recalling the summation (2) developed in conjunction with Figure 6. In the present embodiment the mathematical operation of summation (2) is performed using a moving mask having a plurality of cycles of a substantially sinusoidally shaped pattern of varying amplitude, the integration being performed by the photo detector 150. Specifically, the mask 140 has N cycles of sinusoidally shaped transparency thereon which vary continually in amplitude from zero to a predetermined maximum. As the mask is moved, the photodetector views the parallel elongate projections or images along a substantially sinusoidal viewing line with a peak amplitude which varies with time relative to a base line substantially perpendicular to the said parallel projections cr images on film 120. In the present embodiment, each full cycle of sinusoid is dimensioned to image the set of projections on film 120. However, as will become understood, the invention could be practiced in alternative way, such as by using an integral number of half cycles of sinusoid to image an appropriate set of projections taken over a range of rotational angles which correspond to the number of half cycles of sinusoid utilised.

The geometrical rationale can be better understood with reference to Figure 8 which illustrates a portion of the mask 140 and one cycle of sinusoidal transparency thereof imag ing the set of projections on the film 120. If the instantaneous amplitude of the sinusoid is designated r, it can be shown that a "point absorber" at a point (r, +) in the original object (from which the projections 120 were made) would yield the illustrated sinusoidal pattern on the projections as the object is rotated through 3600 of angles bi (see FIG.

6). Accordingly, the summation representative of each back-projected point of expression (2) is represented by the instantaneous output of photodetector 150. The relatively slow amplitude variation of the sinusoid is equivalent to varying the radius of the reconstructed point and the relatively fast phase variation of the sinusoid (imaged on the projections) is equivalent to varying the angle S of the reconstructed point These variations yield a spiral reconstruction pattern which is obtained on a display or recorder 190 by varying the radius of the scan in accordance with the signal 183A from shaft encoder 183 and varying the angular position of the scan in accordance with the signal 181A from shaft encoder 181.

(If the display has conventional horizontal and vertical deflection means, the appropriate deflection signals are readily obtained from rsin s and rcos f respectively.) The circumference of the sprocketed roller 151 is set equal to the period of one cycle of the sinusoidal pattern on mask 140, so the output of the shaft encoder 181 varies directly with #, as desired. Gearing 82 steps down the rotational rate of the roller 151 by a factor of N.

Since there are N cycles of sinusoid on the mask, the shaft encoder will cycle once for each complete cycle of the mask, and r will thereby vary directly with the sinusoidal amplitude, as desired.

For purposes of understanding the manner in which the apparatus of FIG. 7 generates a back-projected image, the diagram of FIG.

8 illustrates a simple sinusoidal slit as the transparency through which the projections are viewed. It is preferred, however, that the mask also provide a filtering function of the type illustrated in conjunction with FIG. 4.

A portion of a suitable mask is shown in FIG.

13. Laterally across the mask of FIG. 13 the distribution of film transmittance should vary as the function h (x) shown in FIG. 4 and reproduced in FIG. 13. However, since this function is bipolar, a suitable technique must be used to simulate the negative-going portions thereof. For example, the h (x) curve of FIG. 4 could be translated by a constant amount to a higher (positive) reference level so that its transmittance is always positive.

In such case, the output of the photodetector will always be higher than required by the constant amount, so a video bias level can be employed to cancel the resultant undesired "background" brightness level. If desired, a binary distribution of densities (without grey scale) could be utilized, as illustrated in FIG.

14. In such case the shaped apertures on the film have areas which approximate the filter function of FIG. 4.

An alternative scheme for dealing with a bipolar filter function is illustrated in FIGS.

1SA and 15B wherein the transverse sections corresponding to the positive and negativegoing lobes of FIG. 4 are respectively colored, e.g. green and red, respectively, with each having a transmittance which varies laterally across the film in accordance with the filter function of FIG. 4. FIG. 15B shows that portion of the apparatus of FIG. 7 which is utilized in conjunction with the mask illustrated in FIG. 1SA. A dichroic mirror 251 separates the red and green image portions and photodetectors 252 and 253 produce signals proportional to the positive and negative components, respectively, of the filter function.

These signals are coupled to a difference amplifier 254 whose output is, in turn, coupled to the display 190 of FIG. 7. It will be appreciated that various alternative techniques can be employed to achieve the bipolar filtering function. For example, the color "coded" portions of FIG. 15A could be "coded" with orthogonal polarizations and then "read" using a polarizing beamsplitter. Alternatively, spatial coding could be achieved by splitting the incident beam and then employing separate synchronized "positive" and "negative" masks with associated photodetectors whose outputs are subtracted as in FIG. 15B FIG. 16 shows an optical/mechanical technique for generating the mask 140 of FIG.

7. This technique obtains the desired sinusoidal pattern by simulating the projection of point absorbers in an original object as they are rotated for successive exposures. A slotted rod 301 is pivotally mounted at 302 and is driven in an arc by a peg 312 which fits in the slot 303 of rod 301. The peg is movable (by means not shown) radially in a track 313 of a wheel 311 which is rotated synchronously (by means not shown) about its center 314.

A sliding bar 330 is constrained to move in the vertical direction, in this configuration, by guides 331. The bar 330 has a peg 332 thereon which slides in the slot 303 or rod 301.

An unexposed photographic film 350 is moved at a substantially constant speed (by means not shown) along the horizontal direction. The film speed is synchronized with the angular rotational rate of the wheel 311. A member 335 having a vertical slit 336 therein is mounted on the end of bar 330. The film 350 is exposed through the slit 336 by a light source (not shown). The slit is covered with a film having a graded transmittance which corresponds to the function h (x) of FIG. 4, or any desired filter function. Alternatively, the slit could be clear but shaped to have an effective varying transmittance along its length which corresponds to the desired filter function. In operation, as the peg 312 rotates around center 314 each point on the slit traces out a substantially sinusoidal pattern on the film 350. The amplitude of each period of sinusoid depends on the instantaneous radius r of the peg 312. The radius r is slowly increased at a constant relatively slow rate (or can be incremented after each rotation), and the number of rotations of wheel 311 necessary for a full sweep of the radius is determinative of the number of cycles of sinusoid exposed on the film. The distances between point 302, center 314 and bar 330 may be proportional to the respective distances between the X-ray source, the axis of rotation of the object being examined, and the recording surface, so that each cycle of sinusoid pattern simulates the projection of a point absorber at a particular radius in the original object as it is rotated for successive exposures.

As noted above, the slit 336 could alternatively be a shaped aperture and, also, a flashing light source could be provided for discrete exposures. Appropriately coloring or polarizing regions could also be employed to obtain mask patterns such as in FIG. 15A.

Also, a binary mask could be employed at the slit 336. If desired, "positive" film 350 may be used to make the mask 140 (FIG. 5) directly. For a binary mask 140, it will be understood that substitutes for photographic film can be used; e.g. a metal film etched using the exposed film 350 as a pattern, or any suitable material preferably having strength and stability.

The invention has been described with reference to specific embodiments, but it will be understood that variations within the scope of the invention will occur to those skilled in the art. For example, the rotation and/or translation of the optical elements relative to other components of the system could be employed as an alternative form of achieving the desired result, instead of the rotation of the drum 101 of Figure 5 relative to the optical system, for example. Also, in the embodiment of FIG. 5 one or more suitable masks having a "continuous" grey-scale transmissivity could be substituted for the binary approximation masks disclosed. The embodiment of FIG. 7 illustrates the mask as being a movable endless loop, but a mask which reciprocates back and forth could also be used.

Also, the mask could, if desired, be held stationary while the projections are moved, either directly or optically, with respect to the mask. Further, it will be understood that while a mechanical technique for generating the mask is shown, the mask could alternatively be generated by electronic control of an optical display, such as a computer driven cathode ray tube. Finally, while a mask having a pattern in the form of a transparency is preferred, it will be understood that a reflective mask could be employed.

WHAT WE CLAIM IS: 1. Apparatus for generating a two-dimen- sional back-projected image of a slice of an object, comprising: an image carrier having a plurality of substantially parallel elongate optical images thereon, each elongate image having an optical characteristic varying along its length in accordance with the one-dimensional density characteristic (as herein defined) of the said slice of the object obtained at a particular relative rotational angle of the object about a predetermined axis perpendicular to the slice; photodetector means; means whereby the photodetector means responds to a changing portion of the image carrier, the said portion being substantially a sinusoid whose axis is perpendicular to the said elongate optical images; and display or recording means responsive to the output of the photodetector means for displaying or recording the back-projected image.

2. Apparatus for generating a two-dimensional back-projected image of a slice of an object, comprising: an image carrier having a plurality of substantially parallel elongate optical images thereon, each elongate image having an optical characteristic varying along its length in accordance with the one-dimensional density characteristic (as herein defined) of the said slice of the object obtained at a particular relative rotational angle of the object about a predetermined axis, perpendicular to the slice; photodetector means; means whereby the photodetector means responds to a changing portion of the image carrier, the said portion being of sinusoidal or part-sinusoidal form relative to an axis substantially perpendicular to the said parallel elongate images and varying cyclically in sinusoidal amplitude and in position along the said axis; display or recording means responsive to the output of the photodetector means; and means controlling the position of a display or recording element in accordance with the instantaneous position and amplitude of the selected sinusoidal or part-sinusoidal portion of the image carrier in relation to the image carrier as a whole, whereby the successively displayed or recorded elements corresponding to successive outputs of the photodetector means together constitute the image of the said slice.

3. Apparatus as defined in claim 1 or 2, wherein the said image carrier is of cylindrical form the parallel elongate projections extend ing in a direction parallel to the axis of the said cylindrical carrier 4. Apparatus as defined by claim 2 or 3, wherein the image carrier is a photographic film.

5. Apparatus as defined in claim 3, further comprising means for uniformly illuminating the image carrier, means for rotating the cylindrical carrier about its axis, and means for effecting a reciprocating angular movement of the cylindrical carrier about an axis perpendicular to its axis of rotation whereby the amplitude of the said substantially sinu soidal portion of the image carrier varies relative to a base line extending around the cylinder in a plant perpendicular to its axis of rotation.

6. Apparatus as defined in claim 5, further comprising an optical mask between the cylindrical carrier and the photodetector, the mask having an optical transmission characteristic representing a filter function effective to compensate, at least partially, for blurring in the said optical characteristic along the said sinusoidal portion of the carrier.

7. Apparatus as defined in claim 6, comprising a pair of optical masks having transmission characteristics corresponding to positive and negative portions of the desired filter function.

8. Apparatus as defined in claim I or 2, in which the means whereby the photodetector means responds to a changing portion of the image carrier, comprises a mask defining a light-transmitting track in the form of a plurality of cycles of a substantially sinusoidal pattern of varying amplitude, for passing light from the said sinusoidal portion of the carrier to the photodetector, and means for moving the carrier and the mask relative to one another in such a direction that the said photodetector views the carrier by way of a changing portion of the said track and therefore responds to the said changing sinusoidal portion of the said carrier.

9. Apparatus as defined in claim 8, wherein the said mask comprises a movable endless loop.

10. Apparatus as defined in claim 8 or 9, wherein the said plurality of cycles comprising the said track in the mask comprises an

**WARNING** end of DESC field may overlap start of CLMS **.

Claims

**WARNING** start of CLMS field may overlap end of DESC **. other components of the system could be employed as an alternative form of achieving the desired result, instead of the rotation of the drum 101 of Figure 5 relative to the optical system, for example. Also, in the embodiment of FIG. 5 one or more suitable masks having a "continuous" grey-scale transmissivity could be substituted for the binary approximation masks disclosed. The embodiment of FIG. 7 illustrates the mask as being a movable endless loop, but a mask which reciprocates back and forth could also be used. Also, the mask could, if desired, be held stationary while the projections are moved, either directly or optically, with respect to the mask. Further, it will be understood that while a mechanical technique for generating the mask is shown, the mask could alternatively be generated by electronic control of an optical display, such as a computer driven cathode ray tube. Finally, while a mask having a pattern in the form of a transparency is preferred, it will be understood that a reflective mask could be employed. WHAT WE CLAIM IS:

1. Apparatus for generating a two-dimen- sional back-projected image of a slice of an object, comprising: an image carrier having a plurality of substantially parallel elongate optical images thereon, each elongate image having an optical characteristic varying along its length in accordance with the one-dimensional density characteristic (as herein defined) of the said slice of the object obtained at a particular relative rotational angle of the object about a predetermined axis perpendicular to the slice; photodetector means; means whereby the photodetector means responds to a changing portion of the image carrier, the said portion being substantially a sinusoid whose axis is perpendicular to the said elongate optical images; and display or recording means responsive to the output of the photodetector means for displaying or recording the back-projected image.

3. Apparatus as defined in claim 1 or 2, wherein the said image carrier is of cylindrical form the parallel elongate projections extend ing in a direction parallel to the axis of the said cylindrical carrier

4. Apparatus as defined by claim 2 or 3, wherein the image carrier is a photographic film.

integral number of half cycles.

11. Apparatus as defined in claim 10, wherein the amplitude of the said substantially sinusoidal track in the mask varies between zero and a predetermined maximum.

12. Apparatus as defined in claim 9, 10 or 11, wherein the said track in the mask has an optical characteristic, transverse to the path length, corresponding to a filter function such as to compensate, at least partially, for blurring in the said optical images along the said sinusoidal portion of the carrier.

13. Apparatus as defined in any one of claims 8 to 12, wherein the carrier is disposed within an opaque frame.

14. A method of generating a two-dimensional back-proected image of a slice of an object, comprising the steps of providing a plurality of substantially parallel elongate optical images on a carrier, each elongate image having an optical characteristic varying along its length in accordance with the onedimensional density characteristic (as herein defined) of the said slice of the object obtained at a particular relative rotational angle of the object about a predetermined axis perpendicular to the slice; causing a photodetector means to respond to a changing portion of the image carrier, the said portion being substantially a sinusoid whose axis is perpendicular to the said elongate optical images; and displaying or recording the back-projected image as a function of the output of the photodetector means.

15. A method in accordance with claim 14, in which the substantially parallel elongate projections are provided on a cylindrical carrier and extend in the axial direction of the carrier, the carrier being rotated about its axis to cause the sinusoidal portion of the carrier to which the photodetector means responds to move around the circumference of the carrier.

16. A method in accordance with claim 15, in which the axis of the cylindrical carrier is given a varying angle of tilt, during the rotation of the carrier, to provide a variation of sinusoidal amplitude of the said sinusoidal portion to which the photodetector means responds.

17. A method in accordance with claim 14, 15 or 16, in which the photodetector means views the said carrier through a mask having an optical transmission characteristic representing a filter function effective to compensate at least partially, for blurring in the said optical characteristic of the said sinusoidal portion.

18. A method according to claim 14, comprising placing a mask in the light path between the carrier and the photodetector means, the mask comprising an elongate transparent track for the passage of light from the carrier to the photodetector, the track including a plurality of cycles of substantially sinusoidal form; and relatively moving the mask on the one hand and the carrier and photodetector on the other hand, whereby the photodetector views the said carrier by way of a changing portion of the said track and therefore responds to the said changing sinusoidal portion of the carrier.

19. A method as defined in claim 18, wherein the relative movement of the mask and the carrier and photodetector means comprises moving an endless mask with respect to a stationary carrier and a stationary photodetector.

20. Apparatus for generating a two-dimensional back-projected image of a slice of an object, substantially as herein described with reference to the accompanying drawings.

21. A method according to claim 14 for generating a two-dimensional back-projected image of a slice of an object substantially as herein described.