Provision of image data

A method and apparatus are disclosed for providing image data. The method includes the steps of providing incident radiation from a radiation source at a target object and, via at least one detector, detecting an intensity of radiation scattered by the target object. Also via the at least one detector an intensity of radiation provided by the radiation source absent the target object is detected. Image data is provided via an iterative process responsive to the intensity of radiation detected absent the target object and the detected intensity of radiation scattered by the target object.

The present invention relates to a method and apparatus for providing image data of the type which may be utilised to construct an image of a region of a target object. In particular, but not exclusively, the present invention relates to a method of providing such image data using an iterative process making use of an unknown probe function.

Many types of imaging techniques are known for deriving spatial information about a target object (sometimes referred to as a specimen). For example in conventional transmission imaging an object is irradiated by plane wave illumination. The waves scattered by the object are re-interfered by a lens to form an image. In the case of very short wave length imaging (X-rays or electrons) this technique has many known difficulties associated with aberrations and instabilities introduced by the lens which limit the resolution and interpretability of the resulting image. Typical achievable resolution is many times larger than the theoretical limit. Other types of imaging techniques are known but many of these have problems such as resolution limits, long data gathering times or the need for complex and expensive equipment.

A technique for high resolution imaging has been disclosed in WO 2005/106531. This document, which is herein incorporated by reference for all purposes, discloses a method and apparatus of providing image data for constructing an image of a region of a target object which includes the steps of providing incident radiation from a radiation source at a target object. Via at least one detector, detecting the intensity of radiation scattered by the target object and providing image data responsive to the detected intensity without high resolution positioning of the incident radiation or a post target object aperture relative to the target object. Also disclosed is a method for providing such image data via an iterative process using a moveable softly varying probe function such as a transmittance function or illumination function.

Those skilled in the art now refer to the technique disclosed in WO 2005/106531 as the ptychographical iterative engine (or PIE). This is a powerful technique for the recovery of image data relating to an area of an object from a set of diffraction pattern measurements. Each diffraction pattern is formed by illuminating an object with a known wave front of coherent radiation with the requirement that the intensity of the wave front is concentrated within a localised lateral region where it interacts with the object. Examples of such a wave front would be that generated a short distance beyond an aperture when it is illuminated by a plane wave, or the focal spot generated by a convex lens illuminated by a plane wave. The technique is also applicable to scenarios where a target is illuminated by plane wave radiation and a post target object aperture is used to select illumination scattered by a region of the object.

In this sense a diffraction pattern is the distribution of intensity produced by an optical configuration some distance beyond the object and at a plane normal to the direction of propagation of the illumination wave front. This plane is designated as the measurement plane and measurements made at this plane are denoted Ψk(u) with u being an appropriate coordinate vector. It is to be noted that when the distance between the measurement plane and a sample plane is small the diffraction pattern is known as a near-field diffraction pattern. When this distance is large the diffraction pattern is known as a far-field diffraction pattern.

Ptychography relies upon the recording of several diffraction patterns at the measurement plane using a suitable recording device such as a CCD camera or the like. The lateral positions of the object and the localised illumination wave front are different for each pattern.

In order to provide useful image data characteristics of a probe function which might be a transmittance function associated with a post target object aperture or an illumination function associated with incident radiation itself must be known or estimated. This either requires time consuming set up techniques or can lead to inaccuracies if the probe function used is in accurate. Furthermore the iterative process can be time consuming.

It is an aim of the present invention to at least partly mitigate the above-mentioned problems.

It is an aim of certain embodiments of the present invention to provide a method and apparatus suitable for providing image data which may or may not be used to construct an image of a region of a target object and which can be utilised without careful knowledge of a probe function being required.

It is an aim of certain embodiments of the present invention to provide a method and apparatus for providing image data in which an iterative process is used which produces useful results in an efficient manner.

According to a first aspect of the present invention there is provided a method of providing image data for constructing an image of a region of a target object, comprising the steps of:providing incident radiation from a radiation source at a target object and, via at least one detector, detecting an intensity of radiation scattered by the target object;via the at least one detector, detecting an intensity of radiation provided by the radiation source absent the target object; andproviding image data via an iterative process responsive to the intensity of radiation detected absent the target object and the detected intensity of radiation scattered by the target object.

According to a second aspect of the present invention there is provided apparatus for providing image data for generating an image of a region of a target object, comprising:locating means for locating a target object at a predetermined location;a radiation source for providing incident radiation at a target object located by the locating means;at least one detector device for detecting an intensity of radiation scattered by the target object locating means for locating incident radiation or a post-target aperture at one or more locations with respect to the target object; andprocessing means for providing image data via an iterative process responsive to an intensity of radiation detected absent the target object and a detected intensity of radiation scattered by the target object.

Certain embodiments of the present invention provide the advantage that during an iterative process a probe function is itself iteratively calculated step by step with a running estimate of the probe function being utilised to determine running estimates of an object function associated with the target object.

Certain embodiments of the present invention provide the advantage that illumination from an optical set up without a target may be efficiently measured before and/or after analysing a target object. This obviates the need for a probe function to be measured at other times.

Certain embodiments of the present invention provide a method of providing high resolution images using image data gathered via an iterative process and constructing an image therefrom.

Certain embodiments of the present invention provide the advantage that image data indicating characteristics of a target object may be provided which may then be processed as data so as to determine some other characteristic of a target object. As such an image is not necessarily constructed using the image data.

FIG. 1illustrates how a scattering pattern may be developed and used to determine image data corresponding to information about the structure of a target object. It will be understood that the term target object refers to any specimen or item placed in the path of incident radiation which causes scattering of that radiation. It will be understood that the target object should be at least partially transparent to incident radiation. The target object may or may not have some repetitive structure. Alternatively the target object may be wholly or partially reflective in which case a scattering pattern is measured based on reflected radiation.

Incident radiation10is caused to fall upon the target object11. It is to be understood that the term radiation is to be broadly construed as energy from a radiation source. This will include electro magnetic radiation including X-rays, emitted particles such as electrons and/or acoustic waves. Such radiation may be represented by a wave function Ψ(r). This wave function includes a real part and an imaginary part as will be understood by those skilled in the art. This may be represented by the wave functions modulus and phase. Ψ(r)* is the complex conjugate of Ψ(r) and Ψ(r) Ψ(r)*=|Ψ(r)|2where |Ψ(r)|2is an intensity which may be measured for the wave function.

The incident radiation10is scattered as it passes through and beyond the specimen11. As such the wave function of the incident radiation as it exits the specimen will be modified in both amplitude and phase with respect to the wave function of the incident radiation at the pre-target side of the specimen. The scattering which occurs may include Fourier diffraction, refraction and/or Fresnel diffraction and any other form of scattering in which characteristics of the incident radiation are modified as a result of propagating after the specimen. If an array of detectors such as a CCD detector12is arranged a long distance from the specimen then a diffraction pattern is formed at a diffraction plane13. A Fourier diffraction pattern will form if the detectors12are located a distance D from the specimen where D is sufficiently long for the diffraction pattern to be formed effectively from a point source. If the diffraction plane is formed closer to the specimen, by locating the detectors nearer, then a Fresnel diffraction pattern will be formed.

The incident radiation10falls upon a first surface of a target object11. The incident radiation is scattered in the specimen and transmitted radiation propagates through to a diffraction plane13where a diffraction pattern forms.

FIG. 2illustrates the process ofFIG. 1in more detail. The radiation10is roughly focused, for example by a weak lens, so that a region of a first surface of the target object is illuminated. The weak lens may of course comprise any appropriate focusing apparatus such as a set of plates and a voltage supply for a beam of electrons or a reflective surface for X-rays. The weak focusing is sufficient to substantially confine the probing radiation beam. It is thus not necessary to sharply focus radiation although of course strongly focussed radiation could be used. Here the target object provides an object function O(r) which represents the phase and amplitude alteration introduced into an incident wave as a result of passing through the object of interest. The illuminating radiation incident on the target object represents a probe function P(r) which forms an illumination function such as that generated by a caustic or illumination profile formed by the lens or other optical component. P(r) is the complex stationary value of this wave field calculated at the plane of the object. The exit wave function ψ(r,R) defines the scattered radiation as it exits the downstream surface of the target object. As this exit wave propagates through space it will form a diffraction pattern Ψ(u) at the diffraction plane13.

It will be understood that rather than weakly (or indeed strongly) focusing illumination on a target, unfocused radiation can be used with a post target aperture. An aperture is located post target object to thereby select a region of the target for investigation. The aperture is formed in a mask so that the aperture defines a “support”. A support is an area of a function where that function is not zero. In other words outside the support the function is zero. Outside the support the mask blocks the transmittance of radiation. The term aperture describes a localised transmission function of radiation. This may be represented by a complex variable in two dimensions having a modulus value between 0 and 1. An example is a mask having a physical aperture region of varying transmittance.

Incident radiation would thus fall upon the up-stream side of the specimen and be scattered by the specimen as it is transmitted. A specimen wave O(r) is thus formed as an exit wave function of radiation after interaction with the object. In this way O(r) represents a two-dimensional complex function so that each point in O(r), where r is a two-dimensional coordinate, has associated with it a complex number. O(r) will physically represent an exit wave that would emanate from the object which is illuminated by a plane wave. For example, in the case of electron scattering, O(r) would represent the phase and amplitude alteration introduced into an incident wave as a result of passing through the object of interest. The aperture provides a probe function P(r) (or transmission function) which selects a part of the object exit wave function for analysis. It will be understood that rather than selecting an aperture a transmission grating or other such filtering function may be located downstream of the object function. The probe function P(r−R) is an aperture transmission function where an aperture is at a position R. The probe function can be represented as a complex function with its complex value given by a modulus and phase which represent the modulus and phase alterations introduced by the probe into a perfect plane wave incident up it.

The exit wave function ψ(r,R) is an exit wave function of radiation as it exits the aperture. This exit wave ψ(r,R) forms a diffraction pattern Ψ(u) at a diffraction plane. Here r is a vector coordinate in real space and u is a vector coordinate in diffraction space.

It will be understood that with both the aperture formed embodiment and the non-aperture embodiment described with respect toFIGS. 1 and 2if the diffraction plane at which scattered radiation is detected is moved nearer to the specimen then Fresnel diffraction patterns will be detected rather than Fourier diffraction patterns. In such a case the propagation function from the exit wave ψ(r,R) to the diffraction pattern Ψ(u) will be a Fresnel transform rather than a Fourier transform.

FIG. 3illustrates an iterative process according to an embodiment of the present invention which can be used to recover image data of the type which can be used to construct an image of an area of an object from a set of diffraction patterns. The iterative process30illustrated begins with a guess31at the object and a guess32at the form of a probe function used. Subsequently these initial guesses are replaced by running guesses in the iterative process. The initial guesses for the image and/or probe function can be random distributions or can themselves be precalculated approximations based on other measurements or prior calculations. The guesses are modelled at a number of sample points and are thus represented by matrices. Such matrices can be stored and manipulated by a computer or other such processing unit. Aptly the sample points are equally spaced and form a rectangular array. The probe function estimation after k iterations is denoted by Pk(r) and the recovered image after k iterations by Ok(r). The original guesses for the probe function and objection function are thus P0(r) and O0(r) respectively where r is an appropriate coordinate vector.

If the current translation vector relating to the relative positions of the object and the probe function is denoted Rkthen the interaction between the guessed-at object distribution and the probe function is modelled by
ψk(r,Rk)=Ok(r)Pk(r−Rk)  1

This is the current exit wave front. According to embodiments of the present invention an iterative process is used to update the object guess. This is illustrated by the left hand box33inFIG. 3. An updated probe function guess is also iteratively calculated which is illustrated by the right hand box34inFIG. 3.

Referring to the update of the object guess a first step is to determine the exit wave front ψ(r, Rk) at step35. This is carried out using equation 1 noted above. A next step is to propagate the exit wave front to the measurement plane which is accomplished using a suitable model of propagation for the coherent wave front. The propagation is represented by the operator T where:
Ψk(u)=[ψk(r,Rk)]  2

The forward transform T shown as step36generates a propagated wave front Ψk(u) where u references coordinates in the measurement plane. Since Ψk(u) is complex-value this can be written as:
Ψk(u)=Ak(u)exp(iθk(u))  3

Next this modelled wave front must be compared to a measured diffraction pattern. If the guessed-at object is correct then the following equality holds for every value of k.
Ak(u)=√{square root over (Ωk(u))}  4

The modulus of the propagated exit wave front equals the square root of the recorded diffraction pattern intensity. Generally this will not be the case as the guessed-at object will not correctly represent the true object at the sample points. To enforce the equality the modulus of the propagated exit wave front is replaced by the square root of the recorded diffraction pattern intensity as:
Ψ′k(u)=√{square root over (Ωk(u))}exp(iθk(u))  5

At step37the modulus of the propagated exit wave front is replaced by the square root of the recorded diffraction pattern intensity.

The corrected wave front is then propagated back to the plane of the object using the inverse propagation operator:
ψ′k(r,Rk)=−1[Ψ′k(u)]  6

This inverse propagation step39provides the corrected exit wave form ψ′k(r, Rk). An update step40is then calculated to produce an improved object guess Ok+1(r). The update step40is carried out according to:

This update function is labelled U1inFIG. 3which generates the update of the object guess Ok+1(r). The parameter α governs the rate of change of the object guess. This value should be adjusted between 0 and 2 as higher values may lead to instability in the updated object guess. According to embodiments of the present invention the probe function is reconstructed in much the same manner as the object function. Aptly the probe function guess is carried out concurrently with the update of the object guess. (It will be appreciated that the Probe Function could optionally be updated more often or less often then the Object Function). In order to achieve this a further diffraction pattern is recorded in the measurement plane with the target object removed from the system. This further diffraction pattern may be recorded prior to the target object being put in place or subsequent to removal of the target object after the previously mentioned diffraction patterns have been used or may be a combination of diffraction patterns recorded before and after the target object is duly located.

That is to say the diffraction pattern of the probe function itself is recorded. This is denoted as the measurement ΩP(u). The measurement of this diffraction pattern is illustrated inFIG. 4.

At step32P0(r) is chosen as an initial guess at the probe function which may be random or an approximation based on previous other measurements or calculations. Proceeding in a similar manner to the correction/update steps detailed above the probe function guess is propagated with a transform to the measurement plane so that:
Ψk(u)=[Pk(r)]  8
which can be written as:
Ψk(u)=Bk(u)exp(iγk(u))  9

A correction step43is then implemented by replacing the modulus of this propagated wave front with that recorded without the target object in the measurement plane44.

The corrected wave front is then inverse propagated back at step45to give:
P′k(r)=−1[Ψ′k(u)]  11

An update step46makes use of an update function U2which is:

FIG. 5illustrates apparatus for providing image data which may be used to construct a high-resolution image of a region of a target object according to the above-described embodiment illustrated inFIGS. 1 and 2. A source of radiation50provides illumination onto a lens51which weakly focuses the radiation onto a selected region of a target11. The incident radiation has an incident wave function52and an exit wave function53. This exit wave function is propagated across distance D where a diffraction pattern is formed on an array of detectors12. The distance D is advantageously sufficiently long so that the propagated exit wave function53forms a Fourier diffraction pattern in the far-field. The detector array provides at least one detector which can detect the intensity of radiation scattered by the target object11. A locating device54is provided which may be a micro actuator and this can locate the target object at one or more locations as desired with respect to the target object. In this way radiation from source50may be made incident on different locations of the upstream surface of the target11.

Alternatively, in some applications it may be advantageous for the distance D to be sufficiently small so that the propagated exit wave function53forms a Fresnel diffraction pattern on the detector array in the near field.

A control unit55provides control signals to the micro actuator and also receives intensity measurement results from each of the pixel detectors in the detector array12. The control unit55includes a microprocessor56and a data store57together with a user interface58which may include a user display and a user input key pad. The control unit may be connected to a further processing device such as a laptop59or PC for remote control. Alternatively it will be understood that the control unit55could be provided by a laptop or PC. The control unit55can automatically control the production of image data in real time. Alternatively a user can use the user interface58to select areas of the target object for imaging or provide further user input.

In use the source of radiation50illuminates the lens51with radiation. The target object11is selectively located by the actuator54under control of the control unit55. The radiation forms a diffraction pattern detected at respective locations by each of the detectors in the detector array12. Results from these detectors is input to the control unit and may be stored in the data store57. If only one position is being used to derive image data the microprocessor uses this detected information together with program instructions including information about the algorithm above-noted to derive the image data. However if one or more further positions are required prior to finalizing the image data the control unit next issues signals to the actuator54which locates the specimen at another selected location. The actuator may place the specimen at one of many different positions. After relocation a further diffraction pattern formed on the detector array is measured and the results stored in the control unit. As an example the array12may be a CCD array of 1200×1200 pixels. If no further intensity measurements are required image data may at this stage be generated by the control unit in accordance with the two newly stored sets of results using the algorithm above-noted. The raw image data may be displayed or a high-resolution image generated from the image data may be displayed on the user interface1209or remote display on a PC or other such device. Alternatively or additionally the image data itself may be utilised to determine characteristics associated with the target object (for example by data values being compared with predetermined values.

The actuator can be used to move the target object out of the optical path to enable the diffraction pattern without target object to be measured. Alternatively this movement may be effected by another actuator (not shown) or by user interference.

According to a further embodiment of the invention, a diffuser covers a post-target aperture. The diffuser is arranged to diffuse the wavefront from the target such that the radiation incident on the sample is spread more evenly over all diffraction angles in the measured diffraction pattern. By performing the measurements required to recover the illumination function, or probe function, with the diffuser in place, the effect of the diffuser can be automatically recovered as well. Thus, the diffuser may diffuse the wavefront from the target in an arbitrary way, and it is not necessary to know a priori the nature of the diffuser.

The presence of the diffuser leads to a reduction in the dynamic range of the diffraction pattern. As most detectors have limited dynamic range, reducing the dynamic range of the diffraction pattern may allow a more faithful representation of the diffraction pattern to be determined. Furthermore, as the radiation incident on the sample is spread more evenly over all diffraction angles, the incident flux required to provide the image data may be reduced, thereby reducing the possibility of causing damage to the target object.

Any type of diffuser having an arbitrary transfer function may be used. As will be understood by the skilled man, the choice of diffuser will depend on the properties of the radiation used, and the desired diffusion effect. For example, for visible light the diffuser may comprise a ground glass diffuser.

According to a further embodiment of the invention, a diffuser having a known transfer function may be used in conjunction with a known probe function. Such an arrangement allows the diffused probe function to be calculated, allowing the object function to be determined using a precalculated probe function.