BACKGROUND OF THE INVENTION
1. Field of Invention
This invention relates to x-ray tomography. More generally it relates
to an apparatus and method for acquiring three dimensional images showing the composition
and shape of the interior of an object. More particularly, it provides three dimensional
images derived from Compton scattered x-ray signals measured by several detectors
that result when the object is irradiated with a substantially point source of
ultrashort x-ray pulses. The invention also relates to the apparatus for producing
and detecting such point source ultrashort x-ray pulses.
2. Prior Art
Currently most x-ray scanners use a tomographic technique for creating
images. This involves measuring the amount of energy lost along many different
lines of sight that all lie in a single slab. The slab is broken up into small
volumes, or pixels, and based on the line of sight information, the amount of energy
lost in each pixel is calculated. The cross section and density information for
that pixel is then recovered. In practice, this results in a two dimensional image
that has a certain thickness. Three dimensional information is recovered by moving
the object that is being imaged.
Another three dimensional technique has been proposed based on the
concept of photon migration. See, for example, U.S. Patent 4,857,748 issued August
15, 1989. This entails radiating a sample with ultrashort optical pulses and measuring
the time evolution of the transmitted and reflected signals along a line of sight.
Both of these signals include not only directly transmitted or reflected photons,
but also photons which may be scattered several times inside the material and then
reemerge. These photons are said to be diffusing or migrating through the object
and might contain information regarding the structure of the object. This approach
suffers from several problems. First and foremost, most materials are too optically
"thick" to provide any information. Additionally, optical photons can have very
complex paths before they reemerge and the mathematical unfolding of these signals
to determine the structures that have scattered or reflected them is virtually
an intractable problem.
Methods are also known for recognizing in photographic data curves
having pre-determined configurations. For example U.S. patent 3,069,654 to Hough,
issued December 18, 1962, describes apparatus for determining the presence of
straight lines in a photograph. The original use of this technique was to automate
the determination of the presence of linear particle tracks in bubble chamber
The Hough invention recognizes the presence of markers in a photograph
lying along a line in the photograph by first associating each unique marker in
the photograph with a corresponding unique line in a second space. The association
is done so that the lines in the second space form bundles passing through points
(called knots) in the second space only if the associated markers lie on a straight
line. Thus by looking for knots in the second space one locates all the lines on
which the markers lie.
In particular if (x,y) is the location of the marker, then according
to the Hough patent the associated line in the second space is defined by the equation
y' = (x'-x)/y. (See column 1, line 70 to column 2, line 7). It's then a simple
matter of algebra to show that a collection of markers satisfying the linear relationship
y = mx + b has associated lines that all intersect at the so-called "knot" (x',y')
= (-b/m, -1/m). Once the coordinates of the knot (x',y') are determined by inspection
of the lines in the second space, the line in the photograph along which the markers
lie is determined by the equation y = -x/y' + x'/y'.
The above association is known as a Hough transformation and has
been generalized for curves other than straight lines. See for example Duda, R.O.
and Hart, P.E. "Uses of the Hough Transformation to detect lines and curves in
pictures", 15 Comm ACM, 1972, p.11; and "Kimme et al., "Finding Circles
by an Array of Accumulators", 18Comm ACM, 1975, p. 120. Kimme
describes the use of the generalized Hough technique to recognize circles in x-rays,
something that is useful where tumors are spherical. These techniques differ from
the present invention because they seek only details of pro-determined configuration.
BRIEF DESCRIPTION OF THE INVENTION
The present invention irradiates an object with an x-ray beam, and
observes the photons scattered out of the beam into a large solid angle. The number
of scattered photons that arise from any small volume, herein termed a "voxel",
is determined by the Compton scattering cross section for the material in that
volume. This cross section is a known function of the object's electron density
and the x-ray beam's energy spectrum. Namely, the Klein-Nishina spectrum. The
x-ray beam's spectrum is measured, and the density of material in any voxel in
the object is determined by measuring the number of photons undergoing Compton
scattering from that voxel.
This invention employs a method having the steps of irradiating an
object with pulses from a point source that produces ultrashort x-ray pulses and
reconstructing a three dimensional image from measurements of the time evolution
of the Compton scattering from the object at several locations in space. The point
source ultrashort x-ray pulses are produced from a high intensity optical laser
pulse that is used to produce an electron beam that in turn produces the x-rays,
for example by Bremsstrahlung emission.
The invention enables therapeutic x-rays (e.g. high energy x-rays
used for cancer therapy) to be imaged resulting in a three dimensional depiction
of the dose delivered to the patient.
It is an object of the present invention to provide an apparatus
and method for measuring the three dimensional composition and structure of an
object opaque to ordinary light in a non-invasive manner using ultrashort x-ray
pulses of photons that each undergo a single Compton scattering event in passing
through the object and by correlating the time of arrival of the scattered photon
at a detector with its time of emission from its source.
It is another object of the present invention to provide an apparatus
for delivering ultra-short x-radiation doses to an object or patient, monitoring
the radiation re-emitted by that object and reconstructing a three dimensional
image of the object which re-emitted the radiation.
It is yet another object of the present invention to provide a three
dimensional image of therapeutic x-rays dosages received by a patient.
It is a further object of this invention to provide a processor that
is capable of extracting image data from the measured re-emitted x-ray data produced
by Compton scattering of ultra-short x-ray pulses by the object under investigation.
To attain these objects there are two preferred embodiments of the
x-ray source of the invention. According to the first embodiment of the invention
there is provided an imaging apparatus that is comprised of a Ti:Sapphire laser
for generating a narrow beam of ultrashort optical pulses, a photo cathode for
converting the optical pulses into short electron pulses and then accelerating
and focusing the electrons into an anode, which acts as a target and produces ultrashort
x-ray pulses. Six or more detectors, either streak camera type detectors or high
speed photoconductors, are placed around the object to be imaged/radiated, and
the time resolved signals from each is recorded. This time of arrival is correlated
with the time of creation of the x-ray pulse. Finally, processor means are provided
for converting these measured signals and their time of arrival into an image
of a three dimensional object. The particular method for converting these values
is an important aspect of the invention.
According to the second preferred embodiment of the invention, the
imaging apparatus again comprises a high intensity laser, a photocathode electron
gun, and linear accelerator section to produce a high energy short pulse electron
beam. This electron beam is then incident on a target to produce ultrashort x-ray
pulses. Again, six or more detectors are placed around the object to be irradiated,
and the time resolved signal from each is recorded. Processor means are provided
for constructing the three dimensional image and the corresponding x-ray radiation
The invention is further described by its preferred embodiments that
should be considered in connection with the following drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
- Fig. 1 is a block diagram illustrating the interconnection of the components
of a preferred embodiment of the present invention.
- Fig. 2 is a schematic diagram of a high repetition rate ultrashort x-ray pulse
- Fig. 3 shows a higher energy ultrashort x-ray pulse generator.
- Fig. 4 shows a streak tube detector.
- Fig. 5 shows an interdigitated detector.
- Fig. 6 is a diagram showing the time evolution of a single pulse radiating
from an ultrashort x-ray source through an object to a detector.
- Fig. 7 is a diagram showing the geometric arrangement of a field of view volume
for the measurement scheme.
- Fig. 8 is a diagram showing the scattering of pulsed x-rays from a single point
source from three separate locations in the object to be imaged.
- Fig. 9 is a flow chart of an overview of the reconstruction algorithm employed
in the processor of the present invention.
- Fig. 10 is a flow chart of the first construction of the reconstruction algorithm
of the present invention.
- Fig. 11 is a flow chart of the second construction of the reconstruction algorithm
of the present invention to refine the resulting image.
The block diagram in Figure 1 shows an overview of the imaging system.
A picosecond or subpicosecond pulsed laser 1 such as a any sub-picosecond laser
with average power of approximately 100 milliwatts such as a mode locked Ti:Sapp
laser for lower energy/high repetition rate or a synchronously pumped dye laser
system. For higher energy/low repetition rate a multi staged dye laser may be
used or any laser capable of delivering at least one millijoule per pulse with
pulse width less than about one picosecond. The laser radiation is incident on
a photocathode apparatus 3 shown in greater detail in Figure 2. The photocathode
apparatus 3 comprises a beam splitter 5 to deflect a portion of a
pulse from the laser 1 through an optical window 7 onto a photocathode
9 and accelerator section 11. The configuration shown is appropriate
for relatively low energy x-ray generation, typically x-rays having an energy of
about 100 keV. An alternative embodiment provides higher energy x-rays up to typically
50 meV by employing a higher energy source of photons and electrons for the production
of more penetrating x-rays such as type of short pulse electron sources found
in photocathode driven free electron lasers variety used at either Vanderbilt University
or Brookhaven National Laboratories Free Electron Laser facilities and are shown
in Figure 3.
Returning to Figure 2, there is shown an anode 13
accelerator section 11 arranged so that the electrons emitted from the photocathode
9 are accelerated onto the anode. The sudden deceleration of the electrons
as they strike the anode 13 produces x-rays that can exit from the acceleration
section 11 through the x-ray window 15.
The photocathode and anode together comprise the x-ray cathode or
source 17 depicted in Figure 1. The x-rays emitted from the source
17 pass through a collimator 19 to impinge on a field of view volume
of the object 21
to be imaged and then on a plurality of x-ray detectors
23. The collimator 19 is a heavy metal alloy such as those used in
radiation therapy machines. The collimator passes only x-rays in a particular direction.
The x-ray detectors 23 can either be streak camera detector's
as shown in Figure 4 and manufactured by Cordin Cameras, or may be interdigitated
solid state detectors consisting of a metal pattern as shown in Fig. 5 deposited
on a GaAs or other suitable high speed substrate. Typical dimensions between the
digits would be < 5 microns. Such devices are available for purchase either
from Emory University laboratories or from Picometrix. In an inter-digital detector,
metal "digits" are deposited on low temperature GaAs or other high speed substrates
and biased through a low capacitance connector. A signal line 25 also connects
the short pulse laser 1 to the detectors 23, to provide timing signals
that enable correlation of the time of departure of the light pulse from the laser
with the arrival of x-rays at the detectors. The detectors 23 provide signals
along signal lines 27 to an array signal processor 29. These signals
indicate both the intensity of detected x-ray radiation and the time of arrival
of the x-rays as well as the time of emission of the laser pulse.
The detector array signal processor 29 is preferably a Unix
type workstation such as a Sun SPARC station or a Hewlett Packard Unix Station.
The workstation is equipped with conventional data acquisition circuit boards
(not shown) such as those available from the workstation manufacturer or available
as IBM PC compatible boards. In the latter case, the array processor will also
include a small IBM PC or PC clone type circuit board dedicated to running the
data acquisition hardware. The data display, data storage unit, and graphics processor
are all part of the workstation. The central control processor will include a
software program to be described below that will be executing on the workstation
In operation, the short pulse laser 1 generates ultra short laser
pulses (<1 picosecond, preferably from 40 femtoseconds) (40 x 10-15
sec.) to 1 picosecond (10-12
sec.) which are then incident on the photocathode
9. The photocathode then emits a short pulse of electrons which are accelerated
into an anode or target 13. The target, in turn, radiates short x-ray pulses.
Image resolution is directly related to the x-ray pulse width by the relationship:
maximum resolution = (speed of light) x (pulse duration); for a 100 fsec pulse
the maximum resolution is 30 µ. For a 1 psec pulse it is 300 µ. For 1 nsec pulse
it is 30 cm.; the shorter the pulse width the better the image resolution. Typical
x-ray pulse widths are 1-2 picoseconds.
The emitted x-ray short pulses are collimated by the heavy metal
collimator 19. The opening of the collimator is either a circular or square
hole which creates a conical x-ray pattern as opposed to an omnidirectional 4 pi
steradian x-ray pattern. The collimator may be fashioned as heavy metal walls
that absorb all x-ray energy except those that pass through its circular or square
hole. The conically expanding x-ray pulse illuminates the field-of-view volume
which contains the object 21 of interest that is to be 3-D imaged.
The x-ray photons of the very short x-ray pulses are scattered by
the atoms of the target. In general, the level of scattering is a function of the
x-ray cross-section of the target's individual atoms multiplied by the density
of the target's atoms. In this case, since the scattering to be detected will be
Compton scattering, the level of scattering will be a function of the target's
electron density. If the target is a complex, heterogeneous material, such as
organic material (an apple, a lung, etc.), the scattering will be very complex
and therefore a methodology has been invented for detection and processing.
A number of detectors 23 are used to detect the scattered
x-ray pulses. They are placed at various known angles and ranges relative to the
field-of-view volume. In selecting these angles one may take advantage of the
sin2(&thetas;/2) behavior of the Compton scattering pattern. The time
that the scattered short pulse x-rays are detected at each detector is used to
determine the total path length from the x-ray source to the detector.
Since the position of each detector is known to within a tolerance,
and the time evolution of the received signal is known within a tolerance, the
information from an array of detectors is used to create a three dimensional image
of the target or any portion of the target. This is done in the array signal processor
29. As shown in Figure 7, the field-of-view volume 31
may be considered
to be a three dimensional cube where each side 33 is defined as the field
length, fl. The cube is divided into small cubic volumes 35 where each
side of these small cubes has a length, Iν, equal to the product
of the speed of light and the pulse width of the short x-ray pulses. For a pulse
width of one picosecond, 1x10-12 seconds, and a speed of light of 3x108
meters/sec, the side length of the small cube, IV, is 3x10-4
meters or 0.3 millimeters. The total number of these small cubes in the field-of-view
volume is (fl/IV)3. Each of these small cubes defines the
physical boundaries of a voxel that is used to generate a 3-D image.
The array signal processor 29, using a unique processing algorithm
to be described below, calculates the amplitude of the scattered x-ray pulses in
each of the small cubes, and assigns this amplitude to a memory location within
the processor 39 for each of the small voxels in a linear array of data.
The linear array of voxel data is handed off to a standard graphics processor
37 which employs standard 3-D graphics software (e.g. the standard x-windows
3D graphics package) for creating the desired image data. This data may be visually
presented by a data display unit 41 such as a computer monitor and/or stored
by a data storage unit 39 such as a read write optical disk or tape for
A use for the data display capabilities of the invention is to provide
a three dimensional image (by using standard software to provide sections or surface
renderings) of radiation dosages during x-ray therapy.
A central control processor 43 is used to control a laser
modulator to maintain the laser in its short pulse mode and power supply unit
45 , an x-ray controller 47 to allow on/off control of the x-ray
source and current control, the array signal processor 29, the graphics
processor unit 37, and the data storage unit 39. The central control
processor comprises a ROM or RAM having a program that runs on the workstation
that allows the user, perhaps an x-ray technician, to run the system. A general
user interface or GUI (not shown) connects the user to the hardware.
Figures 6 and 7 illustrate geometrically the measurement scheme.
In Figure 6, a point P lies inside the field of view 31 and is a distance
I1 from the x-ray source and a distance I2 from the i'th
detector 49, which is one of the detectors 23 shown in Figure 1.
It takes a photon t = (I1 + I2)/c seconds to go from the
source to point P and then to be scattered to the i'th detector. There are many
voxels P' that have associated path lengths I1' and I2' such
that I1 + I2 = I1'+ I2'. All of these
voxels will make up an ellipsoidal surface of revolution called the shell of the
i'th detector at time t and is denoted shelli(t). As shown, this is
a set of points and not a single point.
In Figure 8, scattering of a single pulse, (u-1), from three arbitrary
points in the FOV is illustrated. Since these points are not assumed to lie on
a single ellipsoidal surface these pulses a,b,c, as received by detector i, are
not time coincident.
The attainable resolution of the system is determined by the x-ray
pulse duration tpulse, the active area of the detectors, and the rise
time of the detectors. The upper limit of this resolution, denoted resmax,
is equal to the relation c / tpulse where c is the speed of light.
The impulse response function of the detectors (assuming they are all identical)
is called h(t). If the time evolution of a single pulse is denoted x(t) then the
output y(t) from a detector measuring a single x-ray pulse directly will be given
by the relation:
y(t) = x(τ)h(t -τ)dτ
In theory the impulse response of the detector could be measured
and the actual signal x(t) could be recovered from y(t). This procedure is difficult
to implement unless the signal to noise ratio is on the order of 100. Consequently,
we call the resolution of our detector the full width at half maximum, or FWHM,
of the response function h(t). If this is less than or equal to tpulse
the resolution of the system will be resmax, otherwise the resolution
of the system will be given by the relation c/FWHM. Furthermore, the size of the
detector will affect the resolution of the system.
In the previous description of the elliptical shells of a given detector,
the detector was implicitly assumed to be a point. If the detector has a finite
size, then any two points on the detector will have slightly different elliptical
shells. The maximum distance between these shells will be the largest dimension
of the detector times the sine of the angle of the maximum acceptance of the detector.
Typically this will be smaller than c/FWHM. If it is not, however, then this distance
is the resolution of the system. In the following discussion, the resolution of
the time signal is defined as the spatial resolution of the system divided by
the speed of light.
Three dimensional image reconstruction involves manipulation of spatial
and time data from all n detectors of the system. This is accomplished by the
processing algorithm. The voxel space will be called the field of view or FOV.
The maximum time we need to consider will be determined by the size of FOV and
will be called tmax. The quantity dt represents the time resolution
of our measurement system and determines the voxel volume. The i'th detector's
measured signal at time t will be sig1[t].
The steps for converting the measured signals into a three dimensional
image are termed the initial setup, the first construction, and the image refinement.
The flow charts depicted in Figures 9, 10, and 11 show these steps in detail.
When the procedure is finished the information in the FOV array is displayed using
standard three dimensional graphics software.
Image data is stored in a linear array. The size of the array is
determined by the field-of-view volume and the obtainable resolution. If the image
array is called FOV then the label or address of each voxel in the image is
defined by its (x,y,z) coordinates using the relation:
voxel(x,y,z) = FOV[z*fl2 + y*fl + x]
where fl is the field length and x,y,z range from 0 to fl-1. The size of FOV is
given by the relation
sizeof(FOV) = ( fl / resolution )3
If the field length is 10 centimeters and the desired resolution is 0.1 centimeters
(1 mm) then the size of FOV must be 1,000,000. If the desired field of view is
not a cube then the size of FOV will by analogy be the volume of the field of
view in the unit system where the resolution has dimension 1.
As shown in Figure 9, the image reconstruction begins by determining
the number of time intervals size_sig to be measured, and setting all the voxels
to zero. The time evolving signal from the first detector is sampled every dt.
The ellipsoidal surface corresponding to each dt is determined, and to each voxel
in FOV that lies on that ellipsoidal surface is added a number equal to the
value measured at the detector divided by the number of voxels that the ellipsoidal
surface contains. This procedure is then repeated for each of the detectors. This
process is essentially a re-normalization of the data, which is repeated until
consistency is achieved. The flow chart for this procedure is shown in Figure 10.
This will yield the first construction of the image. This is an approximation
to the image that becomes exact if there are an infinite number of detectors uniformly
distributed in space.
Next the image goes through an iterative procedure that repeats until
the image is self consistent. As shown in the flow chart of Figure 11, a second
three dimensional voxel space FOV' is set up and cleared. The values of the
voxels from the first image that lie on the "first" ellipsoid of the first detector
are summed together and divided by the number of voxels on that surface. This
yields the integrated weight. Then into each voxel in the FOV' corresponding
to the "first" ellipsoid of the first detector is added the corresponding value
from FOV multiplied by the first sampled value from the detector and divided
by the integrated weight. This is repeated for all ellipsoids and all detectors.
The process is then repeated, going this time from FOV' to FOV. The iterations
continue back and forth until the image in FOV and FOV' are the same. This self
consistent image is the refined image that can then be displayed using standard
three dimensional techniques.
A specific implementation of an algorithm for construction of the
image is given in C-language source code in Table A. This may be compiled on any
standard compiler. Stdio.h and math.h are conventional input/output and mathematics
libraries. This algorithm is capable of handling 106 data points/sec
on a PC, with correspondingly greater speed on a mainframe.
While there have been shown and described and pointed out the fundamental
novel features of the invention as applied to preferred embodiments thereof, it
will be understood that various omissions and substitutions and changes in the
form and details of the device illustrated and in its operation may be made by
those skilled in the art without departing from the spirit of the invention. It
is the intention, therefore, to be limited only as indicated by the scope of the
claims appended hereto.