FR2507466A1 - METHOD AND APPARATUS FOR CONTINUOUSLY FAN BEAM TOMOGRAPHY USING AN OPTIMIZATION FILTER - Google Patents

Abstract

THE INVENTION RELATES TO A CONTINUOUSLY EMITTED FAN BEAM TOMOGRAPHY APPARATUS. IT INCLUDES A SOURCE 12 OF X-RAYS, DETECTORS 16, A GATE THAT MOVES THE SOURCE AND THE DETECTORS AROUND A SUBJECT 14. IT ALSO INCLUDES A MEANS PRODUCING AN OPTIMIZED VALUE FOR THE ABSORPTION OF X-RAYS AT SEPARATE TIME POINTS . THIS MEANS INCLUDES A CONTINUOUS FILTER WHOSE BAND WIDTH IS DEFINED BY THE GEOMETRY OF THE MECHANICAL SYSTEM. ERRORS DUE TO STATISTICAL VARIATIONS IN X-RADIATION ARE THEREFORE MINIMIZED. THE APPARATUS OF THE INVENTION HAS AN IMPROVED SIGNAL-NOISE RATIO AND THEREFORE ALLOWS A REDUCTION OF THE RADIATION DOSE.

Description

The present invention relates to the technique of tomographies and more

  particularly, tomography methods and apparatus which measure, on a plurality of radiation detectors, a continuously emitted beam, the source and detectors moving continuously and circumferentially around the subject being examined. With computer-aided tomography methods and apparatus, images are obtained by placing the subject between a source and one or more radiation sensors, the source and sensors moving together along one or more rotating or lateral axes. a computer produces the image by an indirect means More specifically, one draws from the subject a multiplicity of X-ray measurements, which do not in themselves characterize directly the elements being inside

  of the subject in a known and readable form for a human observer.

  The calculator thus interprets the multiplicity of X-ray measurements taken together in a particular manner in the course of which a readable image is created defining the intended object. A subgroup of tomographic apparatuses relating to the invention is commonly

  designated as a continuously emitted fan-beam type.

  The term "continuously emitted fan beam" indicates that the radiation source continually emits radiation into a circular sector-like tracing beam. In this type of apparatus, there are usually several hundred radiation sensors on the surface. fan-beam path on the opposite side of the subject, these sensors thus receiving the X-ray which has been attenuated along the trajectories followed in the body of the

  These sensors form a curved segment of sufficient length

  to collect all the beam from the source which has followed a path in the body of the subject and has been absorbed by it and to produce distinct output signals. In the prior art fan-beam tomographic apparatus, it has been that the simultaneous acquisition of all X-ray measurements corresponding to each position of the gantry was the best way to obtain the mathematical basis necessary for the reconstruction of the tomographic image.

  prior art, the output signals of the beam sensors

  Thus, they are initially processed one by one by separate repositionable integrators, collectively referred to as the "integration and dump" technique, the signals then being sampled and stored by subsequent elements of the apparatus. With the continuous emission beam tomography apparatus and within the limits of the prior art means, it has been judged that the best estimate of the attenuation of the radiation along each defined path can be deduced from the separate output signals of the integration circuits and for the purpose of collecting as much detector output as possible and, therefore, X-ray signals. Another feature of continuously emitted DC beam tomography apparatus using a computer has been the high cost of the necessarily associated auxiliary circuitry. , adding to that of hundreds of int repositionable precision choppers In general, an auxiliary transfer circuit is required for

  each input channel to receive promptly, during an instruc-

  the integration integrators, and thus allow the input integrators mentioned above to be repositioned rapidly at the end of an integration period and be allowed to continue integration during the interval of integration.

next integration time.

  A stated goal of tomographic devices is to

  reduce the dose of radiation Dose conditions are generally

  Defined by the sensitivity of the X-ray detectors, the geometry of the radiation detectors and the subsequent signal processing apparatus In the prior art, it has been assumed that collecting as much radiation signals as possible (by means of an integrator repositionable for each radiation detector)

  was the best way to minimize the radiation dose.

  However, despite the improvements made to

  in the prior art, the necessary dose still remains

  high, which limits the number of examinations

any subject.

  The invention filters the output signals of the detectors

  from the moving X-ray detectors of a tone machine

  fan-beam pattern continuously emitted by means of known filters defined by defined parameters, the output signals being sampled at a given sampling rate The tomographic image is precisely formed from the radiation values obtained at points distinct timeframes from

  filter output signals, eliminating the need for

  simultaneous sampling of all detector output signals at different time points, as in prior art apparatuses The position of the gantry varies continuously, given portal positions being related to distinct time points The output signals of the filters are sequentially sampled at a sampling rate which typically differs from the distinct time points The radiation values obtained are each a value optimized for-given positions of the gantry according to the output signals of the sequentially sampled filters The accuracy of the optimized radiation value is increased by the eliminates error signals in the output signals of the filters according to the nature of the filters The filters are optimized according to parameters including the bandwidth of the filter, the transient response of the filter, the phase response of the filter, geometric limitations Therefore, the filters minimize the error signals in the output signals of the detectors, which improves the estimation of the device. X-ray absorption at distinct time points For example, it is admitted according to the invention that the maximum frequency of the signal obtained from continuous emission tomographic apparatus is fundamentally limited by the source of the radiation, the dimension of the target to be measured. , the cross-sectional area of the radiation detector, and the geometry and movement of these components relative to each other In addition, it is recognized that the random nature of the photon may be expressed as a noise having a noise bandwidth far exceeding the bandwidth of the remaining tomographic apparatus The invention improves the quality of the signal significantly by processing the signals of the speakers. by means of a time-continuous filter used to eliminate noise, the output signal of which is sufficiently

  sampled before conversion for further processing.

  More specifically, according to the invention, one eliminates a

  significant amplitude of the error signal from the radiation source

  by filtering the signals of the detectors by means of a low-pass filter whose cut-off frequency is at a value lower than the sampling rate The mechanical equipment, including the detectors, produces a signal which is substantially a convolution of

  the source with the cross-section of the detectors The temporal signal-

  The invention provides a low-pass filter which extends its action only to the maximum usable frequency of the bandwidth mentioned above. The sampling rate is determined according to the maximum usable sequence. The maximum usable frequency is selected according to an objective or subjective analysis of a Fourier transform of the variable signal over time on the basis of the criteria stated above. The invention therefore allows an increased signal-to-noise ratio and an increased resolution for the signals that are used in the computation of tomographic images. This improvement is sufficient to allow reconstructing an image from the data obtained by means of a radiation source of a reduced level This ensures a lower dose for the subject and increases the possibility of use vis-à-vis the public tomographic diagnosis. In addition, the apparatus of the invention includes continuous filtering prior to sampling and eliminates the need for separate storage elements (for each sensor) in the devices.

  tomography, which significantly reduces the overall cost of the device.

  In summary, the method and apparatus for continuous beam beam tomography emitted according to the invention make use of

  a source of continuous radiation and several

  The gantry supports and displaces the radiation source and the radiation detectors around a center of rotation passing inside the subject. The source of radiation produces a fan beam (generally known in the art as a uniform fan-shaped radiation in a first plane, having a small width and substantially no divergence in a second plane, and in the foreground an angle d range of sufficient amplitude to radiate the entire offered section of the subject) The detectors are arranged behind the subject to form a sufficiently long curved segment

  to completely intercept the radiation passing through the subject.

  Each detector produces a detector output signal accounting for the received radiation. Next, the detector output signal is filtered by a plurality of detector filters having an input that receives the optimized detector output signals to produce a filter output signal. continuously relative to each detector output signal, resulting in a better estimate, or optimized value, determinable for the total X-ray absorption along a determined path through the subject when the filter output signal is sampled at a particular time. sampling rate using subsequent elements of a continually transmitted fan-beam tomographic apparatus with a processing calculator An image is reconstructed based on an optimized X-ray value for distinct time points which, with respect to the sequential nature of sampling the filter output signals, are time-shifted with respect to the sampling rate, or have a different periodicity. The sampling periods appear at a sampling rate which also determines a practical limit for the bandwidth of the detector filters. The sampling rate is limited to a frequency corresponding to a maximum usable frequency of the detector output signal. The maximum usable output of the detector output signals is determined by the largest and smallest object, or target, to be solved, the size and location of each detector, and the displacement of the detector.

  mechanical equipment in relation to the subject The source of radiation

  the objects to be solved and the cross-section of the detectors are convolved in time to produce a time-varying signal whose Fourier transform describes a group of frequency domain signals having a higher frequency signal. maximum usable is tied according

  subjective analysis or objective analysis known to

  of the higher frequency signal According to the invention, the

  signals outside the bandwidth designated above.

  above are error signals, noise or other unwanted signals and must be minimized. The resulting signal can be processed in a processing computer so as to form optimized signals from the filter output signals. The optimized signals are formed for distinct time points (which typically differ from

  sampling rate), where the distinct time points relate to

  at given positions of the gantry The calculator of

  In a variety of known ways, a tomographic image can be formed; the image is then visualized using a means

appropriate visualization.

  The following description 3 designed for illustration

  of the invention, aims to give a better understanding of its features and advantages; it is based on the appended drawings, among which: FIG. 1 is a schematic representation showing the mechanical geometry of a typical continuously emitted fan-beam tomographic apparatus;

  FIG. 2 is a schematic diagram of a subset

  generalized sampling and reconstruction system according to the invention; Fig. 2A shows the transfer characteristic of an element of the subsystem of Fig. 2; FIG. 2B is the time response of a prior art integration and dump circuit relating to the subsystem of FIG. 2; Fig. 3 is a graph showing signals of interest in the frequency domain; Figure 4 is a block diagram of a single path of the continuous filter according to one embodiment of the invention; Figure 5 is a schematic diagram of one embodiment of the continuous filter of the invention; and Figure 6 is a typical filter output signal

of the circuit of Figure 4.

  Reference is now made to the drawings and, in particular, to FIG. 1, on which is presented a general simplified view of the geometry of a continuously emitted fan-beam tomographic apparatus, in a mechanical configuration generally known as a gantry 10. containing an X-ray source 12 which emits a large continuous x-ray beam for passing through the subject 14 to an array of x-ray detectors 16,

  each having a certain detection area in cross section.

  The fanned beam 18 emitted radiation diverges from the source 12 and moves towards the detectors 16 (the divergence being on a sector-shaped fan angle passing through the subject 14 in a first plane perpendicular to the subject, this sector having a relatively small thickness and having substantially no divergence in a second plane perpendicular to the first plane along the axis of the subject) One seeks to obtain the detection and visualization in the form of images of particular targets located inside of the subject 14, these targets being exemplified by a single target. The source 12 and the array of detectors 16 move together around the subject 14 having an angle of rotation and a direction designated by the reference numeral. 22; The desired information is typically stored by means of rotation at an angle 22 equal to 3600, while the source 12 emits a continuous fan beam 18. The different detectors each provide a continuous signal according to the receiving X-ray photons from the source 12 and having

  crossed the subject 14 while the whole moves continuously-

  The signals of the array of detectors are each directly a function of the volume of photons received, and they are therefore inversely proportional to the absorption of the subject 14

  along each line 15 followed by the X-rays from the source 12.

  The signals produced by the detectors are processed by a data acquisition system 24. The system 24 contains several channels, one for each detector output signal and produces an output signal to a complementary logic system of data acquisition, such as for example multiplexers or digital formatting devices, not shown. Next, the signal is processed by a computer.

  multiple uses or a specialized treatment calculator (also

  not shown) in a predetermined manner so that

  a reconstructed image of a view in axial section

  Full fan-beam graphing is described in more detail in U.S. Patent No. 4,135,247. The above-mentioned subsequent processing of the signals may be

  performed according to the cited patent or by any other known means.

  From FIG. 1, it can be seen that the presence of a target 20 is detected by the shadow that it projects by absorbing the energy of the beam 18 in a visible manner by one of the detectors 16. of the target and its shape are deduced from the absorption level according to the linear integral performed on each trajectory 15 as well as by its displacement with respect to the source 12 and the detectors 16 The reconstruction of the target 20 can be

  performed according to known techniques.

  The method and apparatus of the invention relate to the formation of an optimized value for the following absorption

  each path 15 passing through the subject 14 at time points

  distinct values relating to a given set of values of the angle of rotation 22 of the source 12 and the array of detectors 16 The optimized values corresponding to the distinct time points are interpolated, synthesized or obtained in another way from detector sequentially sampled in a

  image-forming processor, which reconstructs a tomographic image

  It is therefore essential that the detector signals

  They provide these optimized absorption values with precision.

  The process preprocessing functions of the apparatus can be generalized as shown in FIG. 2, where each detector produces an output signal X (t) received by a functional block 22 having a generalized transfer function H (FIG. f) or a time domain response h (t) Block 22 produces a signal y (t) which is periodically and instantaneously sampled by the sampling block 24 according to the sampling signal s (t) so as to produce a sampled signal z (t) More specifically, the sampling signal s (t) is defined by the generally known form:

1 1

  s (t) = T Uo (t Kt a), with T = (1), o

K -OD

  o U is a pulse function, a is a phase constant o

  statistic (see Figure 6) and fo is the sampling frequency.

  The samples of y (t) form z (t) as follows:> o z (t) = y (Kt + a) U (t KT a) (2), K -oo

  of the group of values ly (Kt + a) l are the sampling values.

  The reconstructed output signal y (t) is given by Co X (t) = y (Kt + a) where Kt-a) (3), K = -oo o the functional block 26 has the transfer characteristic

  shown in Figure 2A, or that of an ideal low-pass filter.

  An error 6 (t) can be defined in the sampling and reconstruction process The output signal t (t) of the detector 16 is assumed to have a spectral density S (f) and a statistical phase constant a uniformly distributed over the time interval l 0, T1, supporting the definitions: & (t) t (t) -'t (t), (4), S () s (f) f) + s H (f) (5) ), SL (f) = St (f) = O and SH (f) = O, = S (f), f for Ill <2 o elsewhere fo for I 1 f <2 f

for If {_> -

  The statistic mean squared error function ú 2 (t), that is: + foe 2 (t) =) -fo (7) I lH (f) I 2 SL (f) df + f l + H (f) 25 (f) ), which, once reduced, gives the slightest error in sampling and reconstruction, is minimized when: H (f) 1, f for If1 <r (8) f = 0, for fl_ so as to produce an error which is: ## EQU1 ## which incorporates any power signal of t (t) outside the reconstruction region, which has been defined as It is thus understood that, according to one embodiment of the invention incorporating linear filtering for all the distinct time points (a not being limited to a particular value), the o

(6 A)

(6 B).

  the best reconstruction of t, (t) is in the bandwidth _f if l 2 '2 l for a given sampling rate f = The best linear estimator t (t) is thus obtained when the function H (f) of the block 22 consists of that of an ideal low-pass filter, shown in FIG. 3 at 40, which passes all the signals of a frequency equal to or less than the cut-off frequency of the filter and rejects all the signals of a frequency greater than the cut-off frequency, and with an error given by the high frequency power of -X (t) as defined by equation (9) However, if t M (t) has no high power frequency, SH (f) = 0, and by

  therefore, 2 (t) = 0 for an optimal H (f) function.

  When h (t) is h 2 (t) as shown in Figure 2 B for the typical integration and dump response of the prior art over a period T, the transfer response of block 22 is Sin tf TH 2 (f) = (10), 27 T represented by the curve 42 in FIG. 3, and can be compared in the form of the wave 42 of FIG. 3 with the optimal filter response 40, revealing signals Thus, to minimize the energy of the external signals, e.g. the photon noise power shown below, the optimal filter is an ideal low-pass filter. In other words, any signal that G (f), shown in FIG. 2A, and H (f) above the sampling frequency (above SL) pass will cause the addition of an unrecoverable error The sampling rate f is chosen so that it is at least twice as large as the highest useful frequency of i (t) from the sensor 16

  according to the Nyquist criterion It is possible to select

  tentatively or subjectively the highest useful frequency component (considering the device parameters mentioned above) according to the overall shape of the characteristics of the

  detector or target in the frequency domain.

  The overall shape of the signal characteristics of

  target in the frequency domain is given according to the trans-

  formed of Fourier of the respective time-varying signal, which is the convolution of the cross-section of the source with the cross section of the target when both move relative to each other during the rotating sweep period of source and detectors relative to the patient A typical representation in the frequency domain for the signals present in the tomography apparatus considered is shown in FIG. 3 As an illustration, a hypothetical broadband signal obtained from FIG. an elongate source having time-domain irregularities is represented in the frequency domain by curve 48 of FIG. 3 More generally, the low-frequency limit is defined by the maximum duration of absorption, or projected shadow by the object, during the rotation, so that, for example, a

  cross-section of the skull following a detection target almost

  gential will present a continuous absorption during the gantry revolution, thus bringing a continuous component, which defines the condition of low frequency The condition of higher frequency is the limit imposed by the acuity or the speed of the variations of the

  convolution signal varying in time.

  The main source of errors in the reconstructed signal is the inherent uncertainty of the source's emissions, eg the irregularity with which X-rays are produced by a radiation source, while the noise of electronic equipment is in general relatively minor While the photonic noise is broadband, the signals produced from the mechanical equipment that appear at the output of the detectors have a limited bandwidth which is a function of the source to be viewed at the The invention improves the accuracy of the reconstructed signals by restricting the bandwidth of the electrical signals that the apparatus passes on the basis of the maximum bandwidth that is defined by the source and

  mechanical geometry of the tomographic apparatus as described above.

  above, and she rejects, as being an unwanted noise, the signal

  remaining from the detectors.

  In FIG. 3, it is shown, according to the invention, that the performance of the apparatus can be substantially improved by providing a filtering circuit set to allow mainly the convolution signal 48 produced at the output of the detectors, and to minimize the contribution of the photonic noise 44 occurring beyond the maximum useful frequency of the convolution signal A

  typical filter having this description is given by curve 46,

  which has the characteristic of a three-pole "Butterworth" type filter having a point at 3 d B at approximately 380 Hz when the period

  Sampling rate is 1 millisecond.

  An embodiment of a channel of the data acquisition system, according to the filter of the invention, comprises an amplifier

  detector in the amplifier filter 70, shown in FIG. 4.

  The remaining circuits 54 for calibration and protection 34 for each bus, in the same way as in the prior art, or according to other circuit variants can be made according to known methods and apparatus. 3 d B filter, as well as its other characteristics, for example for a Butterworth filter, Chebyshev, an elliptical filter or other type of filter, are established at the discretion of the manufacturer in known manner according to the desired phase characteristics, frequency and time of the data acquisition system, the mechanical system, the subsequent processing of the signals to produce an image

  tomography and the total cost of the device A choice-

  23 filtering characteristics, in relation to the criteria mentioned above, will produce a signal with a

improved signal-to-noise ratio.

  One embodiment of the continuous filter according to the invention is shown in detail in FIG. 5. The detector produces an output current Is which is applied via the input 60 via a resistor R 1 to the gate of a differential torque. of field-effect junction transistors Q1, Q1 Bcontained in a common enclosure 62 in order to have more closely tuned operation over a range of temperatures The protection circuit (34 in FIG. 1) is implemented by a circuit CR 1 containing back-to-back diodes D1A and D1B placed between the Q1A gate and the ground The pair of field effect junction transistors is biased at -12V by resistors R and R 5 derived from the earth by means of a capacitor C 3 The grid input of Q 1 B is connected to earth so as to establish a zero-volt operating point for the circuit of FIG. 5 The load resistors R and R 3 respective drain of QA and Ql B are c connected to the + 12 V voltage via a common resistor R 7 derived by a capacitor Cg The drains of the pair QLA and Q 1 B are connected to the noninversion and inversion inputs of the operational amplifier U 1 which is available on the market under the reference "TL 062" A resistor R 6 and a capacitor C 2 of a compensation network of the amplifier U 1 are connected between the inputs of the amplifier U 1 The pair of transistors field effect junction acts as a high impedance input stage for

  the amplifier U 1; the pair Ol A and Q 1 B and the operational amplifier

  U 1 operate in concert to form an operational amplifier with high input impedance. A filter network consists of resistors R R, RR and R of capacitors 8 '9 10' 11 12> cl) C 4, C 5, C 6 and C 7, of an operational amplifier U 2 (currently

  available on the market under the reference "741"), as well as the

  previously mentioned operational indicator U 1 which operates in

  relationship with the pair of field effect junction transistors.

  The output signal of the filter V appears at 64, and comprises the output signal of the operational amplifier U 2 filtered by the network R 13 in combination with the capacitor C to operate in combination with the previous circuit components, and thus produce a determined overall filter response The characteristics of the filter of FIG. 4 are obtained from the known methods for producing a low-pass Butterworth filter having a 3 dB point at 380 Hz and an overall gain of V / 1.5. 2 x 107 below bone 380 Hz A predetermined amplitude calibration signal that is produced by the calibration means 54 of Figure 4 is provided by line 66 to the capacitor C 2; when the calibration signal is not

  not supplied, the calibration input 66 is grounded.

  By way of example, the following numerical values are given for the resistances R 1 to R 13 and the capacitors C 1 to C 9 R 1 = 2 k / t R 1 = 35.2 k P. R 2 = R 3 R 4 200 kl AR 12 200 Ml 1 R 5 = 25.5 kf R 13 10011 R 6 = 15 k ti Ci C 4 100 p FR 8.2 k ACC 200 p F

7 2 7

  R 8 = 17.96 k AC 3 C 9 5, 6 u FR 9 = R 10 = 48.84 kP, 5 6 C 8 I = F The invention allows the output signal of the filter to be sampled continuously at a desired rate, typically at a higher rate than that specified by the Nyquist criterion as a function of the highest desired frequency, so that, for example, if the highest frequency is about 380 Hz, it is sufficient to a period

  In addition, sampling rates of 1 millisecond

  The output signal 70 of the filter, after processing by the digital-to-digital converter 32, is represented by the signal 80 in FIG. 6, with sample points which appear at 82, 84 and 86 between time intervals -T 1 and T 2 Each of the filters described above outputs, in response to a respective input signal from detectors

  respective apparatus for continuous beam-beam tomography

  nally emitted, a continuous signal providing an optimized value of the absorption of rays along the path formed between the radiation source and the respective detector at distinct time points The distinct time points are offset in time, or have different periodicities, in relation to the said period

  at least some of the filter signals.

  The further processing, the digital formatting and the visualization of the signal coming from each channel of the data acquisition system are carried out by means and

  known techniques Further improvements to the reconstruction

  truction of the image in the attached processing computer are obtained because of the excess information produced by the increased sampling rate beyond the minimum Nyquist rate, as well as the decrease of the error signal As a result of the randomness of the photons in the filter output signal, these improvements can be obtained in a manner known in the art. The construction of reconstructed signals optimized by continuous filtering applied to detector signals with more complex spectral distributions and in devices using sampling rates other than twice the frequency

  highest possible use belongs to the field of the invention.

  It is also within the scope of the invention to sufficiently oversample the output signal of the filter so that part of the filter described above or additional filter or process and correction apparatus,

  may be included in the treatment calculator mentioned above.

  For example, it can be formed inside the treatment computer a filter according to the methods and apparatus known in the digital filtering to add several additional poles, or to provide phase correction characteristics, according to

  characteristics of the particular filter described above

  killing an embodiment of the invention.

  Of course, those skilled in the art will be able to imagine

  from the process and the apparatus of which the description has just been

  given merely by way of illustration and by no means as a limitation, various other variants and modifications not departing from the scope

of the invention.

Claims (11)

R E V E N D I C A T IO N S   1 Continuous beam beam tomography apparatus   issued to resolve targets in a subject, which is   characterized in that it comprises: a radiation source (12) producing X-ray photons in a continuously emitted fan beam (18); a plurality of detectors (16) arranged in a network and arranged to receive said X-ray photons in the plane of said fan beam, each of the detectors producing an output signal as a function of the received X-ray photons; a gantry for supporting and moving the radiation source and the detectors at a certain speed about a center of rotation disposed within the subject (14); a plurality of filters (22, 26, 70) each inputting said output signal from one of said detectors; sampling means (24) receiving at its inputs   the output signals from the filters and outputting a sample of   sequential sampling of the respective input signals received at its   sequential sampling taking place at an exchange rate of   predetermined lenght; each of the filters being designed to output,   in response to its respective input signal, a continuous signal   providing an optimized value of radiation absorption along the path connecting the radiation source to the respective detector at distinct time points; processing means which responds to said output signal   the sampling medium and the position of the gantry crane an image; and   visualization means for displaying visual- this image.   Apparatus according to claim 1, characterized in that at least some of the distinct time points are offset   in time with respect to said sampling rate.   A continuously transmitted beam beam tomography apparatus for resolving targets in a subject, characterized by comprising: a radiation source (12) producing X-ray photons in a continuous fan beam; a plurality of detectors (16) each producing a signal   output as a function of the received X-ray photons, the detec-   transmitters being placed in a network arranged to receive said X-ray photons in the plane of said fan-shaped beam; a gantry for supporting and moving the radiation source and detectors at a certain speed about a center of rotation within the subject (14); sampling means (24) having a plurality of inputs and an output which produces a sampled output signal according to a sequential sampling of respective input signals received at said inputs, the sequential sampling being performed at a certain rate sampling; a plurality of filters (22,26,70) each receiving at its input said output signal of each respective detector and being adapted to produce a continuous output signal relating to each output signal of a respective detector, wherein the filter has a frequency cut-off circuit enabling it to substantially reject signal frequencies above said cutoff frequency; processing means for reconstructing an image according to each of the filter output signals; and display means for displaying visually the image.   Apparatus according to claim 1 or 3, characterized in that said cutoff frequency is determined according to an object to be solved and the movement of the gantry in association with the size and position of each of the detectors; in that the emissions from the source, the object to be resolved and the cross-section of the detectors are convolved in time to produce a time-varying signal whose Fourier transform describes a group of time domain signals having a maximum usable frequency which is a function of said largest object, respectively; and in that said cutoff frequency   corresponds to said maximum usable frequency.   Apparatus according to claim 4; characterized in that said detector filters pass signals at a frequency equal to or less than said cutoff frequency and reject all signals at a frequency higher than said cutoff frequency.   Apparatus according to claim 4, characterized in that   that said detector filter has a pass filter characteristic   Butterworth stockings at three p 8 les.   Apparatus according to claim 1 or 3, characterized in that each detector filter further comprises an amplifier detector (70).   Apparatus according to claim 4, characterized in that it further comprises conversion means (32) which performs selective sampling between said detectors in a predetermined manner corresponding to a rate greater than twice the   periodicity of the maximum usable frequency.   Apparatus according to claim 8, characterized in that   that said sampling conversion means comprises a converter analogue-digital   Apparatus according to claim 1 or 3, characterized in that at least a portion of said filter detector is   in the form of a digital filter (70).   Apparatus according to claim 10, characterized in that said digital filter comprises phase correction characteristics which are a function of the characteristics of said detector filters. Apparatus according to claim 1 or 3, characterized in that it further comprises calibration means (54) forming a calibration signal received by each of said detector filters at said filter input.   Apparatus according to claim 1 or 3, characterized in that it further comprises filter protection means (34).   connected to each of the filter inputs.   14 Operating method of a tomography machine   continuous fan-beam emitted using an optical filter   implementation as described in claims 1 to 13, characterized   in that it comprises the following operations: producing X-ray photons in a continuous fan beam using a source (12); receiving said photons in the plane of the fan beam using a plurality of detectors (16) forming a grating and each producing an output signal as a function of the photons received at the source and the detectors being mounted on a gantry which moves them at a certain speed around a center of rotation placed inside a subject (14); receiving the output signals of the detectors by means of filters (22, 26, 70) receiving the output signals of the filters in a sampling means (24) which outputs a sampling   sequence of its respective input signals according to a sampling rate   predetermined sampling each filter being designed to produce, in response to its respective input signal, a continuous signal giving an optimized value of the radiation absorption along the path connecting the source to the respective detector at distinct time points   construct-an image using a means of   responding to the output signal of the sampling means and the position of the gantry; and   display the image using a display means.