GB2403616A

GB2403616A - Diffraction pattern imaging using moving aperture.

Info

Publication number: GB2403616A
Application number: GB0315245A
Authority: GB
Inventors: John Marius Rodenburg; Helen Mary Louise Faulkner
Original assignee: Sheffield Hallam University
Current assignee: Sheffield Hallam University
Priority date: 2003-06-30
Filing date: 2003-06-30
Publication date: 2005-01-05
Also published as: GB0315245D0; WO2005004188A2; WO2005004188A3

Abstract

A method of constructing or obtaining image data from an object - such as that measured in a far field electron microscope - comprises analysing intensity data of a diffraction pattern from the object arising from an aperture, the aperture being movable between, for example, first and second aperture positions. The analysis, at plural aperture or slit positions, may comprise Fourier transformation, phase or wavefunction estimation. For example, the phase and measured intensity for a diffraction pattern may be combined to form a wave function that may be transformed to form further wavefunctions. Apparatus for performing the method may comprise a coherent radiation source 1001, emitting radiation that interacts with object or specimen 1003 giving object wave function 1004; displaceable aperture 1005 further interacts with the object radiation, giving complex, exit wave function 1006. Aperture 1005 may be moved by displacement actuator 1007. The diffracted output radiation 1008 is then measured in intensity by CCD detector 1009 before processing to produce image data.

Description

24036 1 6

IMPROVEMENTS TO FAR-FIELD IMAGING

Field of the Invention

The present invention relates to far-field imaging, and in particular to improvements to far-field imaging in electron microscopy.

Background to the Invention

Microscopy is used to investigate the structure of objects that cannot be resolved by the eye. Light microscopy is known, using lenses to magnify To radiation in the form of light, and different techniques of electron microscopy are used to achieve higher magnification and investigate other aspects of an object, for example crystal structure.

The limits to the resolution of microscopy can be approximated by the Abbe equation, where: 0.6127 d= . (1) nslnct where d = smallest distance that can be resolved = wavelength n = refraction index 2 0 0( = aperture angle It can be seen from equation 1 that to obtain as low a value for d as possible, the wavelength should be small, n should be large and the aperture angle or should be large.

Electron microscopy can resolve smaller distances than light microscopy because a wavelength of a beam of electrons can be much lower than a wavelength for visible radiation. For example, a beam of electrons at 100 keV has a wavelength of around 0.0037 nm, compared to a wavelength of visible P1 059.spec radiation in a range of the order of a few hundred nm. This allows for resolution of much lower values of d than light microscopy.

However, in practice it is difficult to achieve the theoretical values of d owing to limitations of electron microscope apparatus. Referring to figure 1 herein, there is illustrated schematically the prior art problem of achieving a low value for d. An electron microscope comprises a source of electrons 101 for an electron beam 102, 103 and one or more lenses 104 to focus the electron beam 102, 103.

The lens 104 is typically a magnetic lens or an electrostatic lens. In this example, the lens 104 is configured to focus the electron beam on the image plane 107.

Aberrations in the lens prevent the beam from coming to a focus at a sharp point. Beams 103 that are paraxial (that is, close to an axis 108 of the lens) come to a Gaussian focus 105 on the image plane 107. However, beams 102 that are at higher angles come to a focus 106 prematurely, and so the image on the image plane 107 is not fully focussed. Prior art solutions have included using apertures to remove high angle beams 102. However, this introduces diffraction of the electron beam as it passes through the aperture, and also limits the resolution of the microscope, as high angle beams are required to obtain low o values for d. For an electron microscope operating at 100 keV, the value of)< is around 0.037 A, but values of d that can be obtained are much higher owing to the removal of the high angle electrons from the beam by the aperture.

A further problem in obtaining meaningful data from high angle beams is the z5 stability of the lenses. Magnetic or electrostatic lenses require large power supplies, and minute fluctuations in the power supply lead to fluctuations in the lens. High angle beams are required to interfere with transmitted beams in order to obtain meaningful data, but this interference, especially for high-angle beams, is difficult to establish and remain constant in the presence of lens instabilities.

The largest angle up to which meaningful data can be obtained is known as the information limit. Chromatic variations in the beam can similarly restrict the P 1 059.spec information limit, because changes in wavelength alter the path lengths of high angle beams, thus dephasing them with respect to each other.

Referring to figure 2 herein, there is illustrated schematically Gabor holography. An electron source 201 is used to produce an electron beam 202.

An aberrated lens 203 is used to bring the beam to a focus 204 at a distance from an object to be imaged 205. The electron beam 202 is transmitted through the object, and interactions with the object 205, such as electron scattering, alter the characteristics of the electron beam 202. By using a reference wave, it is 1 C considered theoretically possible to deconvolve a diffraction pattern formed in the far field plane 206 to obtain an exit wave function of the beam after interaction with an object, and hence to image the object. However, holographic methods have some drawbacks relating to the number of measurements that must be taken to deconvolve the diffraction pattern formed in the far field, and the detector size required is prohibitively large if significant improvements to the resolution are to be obtained. In the Gabor geometry, the object must be substantially transparent (weak phase) in order to provide a strong reference wave, whereas this usually not true in practice. The diffraction pattern formed in the far-field is sometimes referred to as a Gabor hologram, or a Ronchigram. The diffraction plane on which the diffraction pattern is formed is also referred to as the microdiffraction plane or the nano-diffraction plane.

Variations on this technique allow some information to be obtained about the object provided that the wave function of the far-field diffraction pattern can be measured and aberrations of the lens are known. However, whilst it is considered that the far-field diffraction pattern contains a large amount of information about the object, it has been very difficult to extract this information.

The wave function of the far-field diffraction pattern comprises a modulus component and a phase component, but only the intensity of the far-field diffraction pattern can be measured, which corresponds to the square of the modulus component. Without knowing the phase component of the wave P1059.spec function, it is difficult to work out the wave function of the electron beam as it exits in the object to be imaged.

Referring to figure 3 herein, there is illustrated schematically a prior art technique for obtaining information about the imaged object from a far-field diffraction pattern. An incoming beam of radiation 301 is incident on an object to be imaged 302. The transmitted beam 303 has interacted with the object and has a wave function 304. A far-field diffraction pattern 306 is formed in the far- field diffraction plane 305. The intensity of the far-field diffraction pattern 305 can JO be measured. By estimating a phase component of the far-field diffraction pattern and knowing the intensity, a wave function for the far-field diffraction pattern 306 can be estimated. An estimated wave function for the exit wave of the radiation as it exits the object is then determined by inverse Fourier transformation of the estimated wave function for the far-field diffraction pattern.

The estimated wave function for the exit wave of the radiation as it exits the object can be modified using a measured intensity of the exit wave function of the radiation as it exits the object. The algorithm used is known as the Gerchberg- Saxton algorithm. Iterations of this process solve the wave function for the exit wave of the radiation as it exits the object. However, to measure the intensity of the exit wave function of the radiation as it exits the object requires use of an imaging lens, with the resolution constrains discussed above, and so this process cannot be used to obtain high magnification information about the object.

Referring to figure 4 herein, there is illustrated schematically the prior art Fienup algorithm for obtaining a wave function of radiation. An object to be imaged 401 has a wave function. It is known that the wave function of an area outside the object 402 is zero. The area of the object 401 over which the wave function is greater than zero is known as the support. An intensity of a diffraction pattern 404 can be measured in the far-field. As with the Gerchberg-Saxton algorithm, an estimate is made of a phase of a wave function of the diffraction pattern in the far- field, and the estimate of the phase is combined with the known intensity to estimate a wave function of the diffraction pattern. Using similar P1 059.spec iterative techniques to Gerchberg-Saxton, an estimate of a wave function of the object can be made. The estimate is corrected at each iteration by removing data from the regions outside the support 401 where the wave function is known to be zero 402.

This method has been demonstrated as a possible means for performing lensless microscopy, although it suffers many major problems. Firstly, an aperture must be employed, an area of the aperture relating to the support, and an area outside the aperture relating to the area outside the support. The To aperture must be sharp and of irregular shape, otherwise certain ambiguities can arise during the reconstruction of the image. In the presence of noise, convergence is not guaranteed and cannot in general be checked. Furthermore, the requirement of a finite support means that a large field of view cannot be investigated, whereas in most practical situations it would be advantageous to image large areas of the object function.

Summarv of the Invention The inventors have devised a method for farfield imaging that includes an aperture that can be scanned across an object to be imaged, or located in very near proximity to the specimen. Radiation is passed through the object and the aperture to form a diffraction pattern in the far-field. The intensities of the diffraction patterns are recorded for at least two aperture positions. Using the intensity measurements and known information about the aperture, an exit wave function of the object is determined. The exit wave function of the object is used to provide high resolution information regarding the object.

According to a first aspect, there is provided a method of constructing image data for a region of an object comprising: JO analyzing an intensity data of a diffraction pattern arising from said region, said intensity data arising from a function of a known aperture, wherein said aperture can be moved to at least two different positions relative to said object.

P1059.spec Preferably, said intensity data of said diffraction pattern is measured in a

far-field of an electron microscope.

Preferably, said analysis comprises at least one Fourier transformation.

Preferably, said analysis is an iterative process.

Preferably, said analysis comprises estimating a wave function.

Preferably, said analysis comprises only using data where a value for an aperture transmission is substantially greater than zero.

Preferably, an estimated phase of said diffraction pattern is combined with said intensity data of said diffraction pattern to form an estimate of a wave function of said diffraction pattern.

Preferably, said analysis comprises transforming said estimate of said wave function of said diffraction pattern to obtain an estimate of a wave function of said 2 0 region of said object.

Alternatively, an exit wave function of said region of an object is estimated.

Preferably, said analysis comprises transforming said estimated exit wave 2 5 function of said object using a known aperture transmission function.

Preferably, said analysis comprises: correcting a wave function of said diffraction pattern using said intensity 3 o data of said diffraction pattern; and preserving a phase of said wave function of said diffraction pattern.

P1059.spec Preferably, said diffraction pattern arises from interaction of radiation from a radiation source with said object.

According to a second aspect, there is provided a method for obtaining image data for an object comprising: (i) obtaining a first diffraction pattern of said object where an aperture is in a first position; and (ii) obtaining a second diffraction pattern of said object where said aperture is in a second position; and (iii) measuring an intensity of said first diffraction pattern; and (iv) measuring an intensity of said second diffraction pattern; and (v) approximating a phase of said first diffraction pattern; and go (vi) combining said phase and said measured intensity of said first diffraction pattern to form a wave function of said first diffraction pattern; and (vii) transforming said wave function of said first diffraction pattern to obtain an estimate of a wave function of said object where said aperture is in a first position; and (viii) transforming said estimate of said wave function for said object where said aperture is in said first position to an estimate of a wave function for said object where said aperture is in said second position; and P1 059.spec (ix) transforming said wave function of said object where said aperture is in said second position to obtain an estimate of said wave function of said diffraction pattern where said aperture is in said second position; and (x) modifying said wave function of said diffraction pattern when said aperture is in said second position using said measured intensity of said second diffraction pattern; and Preferably, the method comprises (a) performing the inverse operation of step (ix); and (b) transforming a new estimate of said wave function for said object where said aperture is in said second position to a new estimate of a wave function for :5 said object where said aperture is in said first position; and (c) performing an inverse operation of (vii); and (d) modifying a new estimate of a wave function of said diffraction pattern 2 o where said aperture is in said first position using said measured intensity of said first diffraction pattern; and (e) repeating steps (vii) to (x) and steps (a) to (d) to obtain a refined wave function of said object where said aperture is in a first position, and a refined As wave function of said object where said aperture is in a second position.

Preferably, said transformations of steps (ix) and (c) comprise a Fourier transformation.

Preferably, said transformations of steps (vii) and (a) comprise an inverse Fourier transformation.

P1 059.spec -9 - Preferably, said transformation of steps (viii) and (b) comprises dividing an estimate of a wave function for said object by an aperture transmission function of said aperture.

Preferably, said division is not performed where said aperture transmission function of said aperture approaches zero.

Preferably, said aperture transmission function of said aperture comprises complex data.

Preferably, said diffraction patterns are obtained where said aperture is in more than two positions.

Preferably, said phase of said first diffraction pattern is preserved during step (d).

Preferably, said phase of said second diffraction pattern is preserved during step (x).

According to a third aspect, there is provided a method of constructing image data comprising: (a) measuring an intensity of a first diffraction pattern arising from a first aperture position; and (b) measuring an intensity of a second diffraction pattern arising from a second aperture position; and (c) estimating a phase of said first diffraction pattern; and P1059.spec (d) combining said estimate of said phase with said intensity measurement of said first diffraction pattern to form a wave function of said first diffraction pattern; and (e) transforming said first diffraction pattern wave function to obtain an estimate of a wave function of an object; and (f) updating said estimate of said wave function of said object using a first known aperture position; (g) determining a wave function of said object at said second aperture position; (h) transforming said second object wave function to obtain an estimated wave function of said second diffraction pattern; and (i) comparing said estimated wave function of said second diffraction pattern with said measured second diffraction pattern; and 2 0 (i) altering an intensity component of said estimated wave function of said second diffraction pattern, to match said measured intensity of said second diffraction pattern, whilst preserving a phase component of said estimated wave function of said second diffraction pattern, to obtain a revised estimate of said second wave function of said second diffraction pattern; and (k) transforming said second revised estimate of said wave function of said second diffraction pattern, to obtain a revised wave function of said object at said second aperture position; and (I) determining a revised wave function of said object at said first aperture position; and P1059.spec -1 1 (m) transforming said revised wave function of said object at said first aperture position, to obtain a revised wave function of said first diffraction pattern; and (n) altering an intensity component of said revised wave function of said first diffraction pattern, to match said measured intensity of said first diffraction pattern, whilst preserving a phase component of said revised wave function of said first diffraction pattern, to obtain a modified wave function of said first diffraction pattern; and (o) repeating steps (e) to (n) to obtain a refined wave function of said object at said first aperture position and a refined wave function of said object at said second aperture position.

s Preferably, said transformation of steps (e) and (k) is an inverse Fourier transformation.

Preferably, said transformation of steps (h) and (m) is a Fourier transformation.

Preferably, said transformation of steps (g) and (I) comprises dividing an estimate of a wave function for said object by an aperture transmission function of said aperture.

Preferably, said aperture transmission function of said aperture comprises a complex wave function.

Preferably, the method measuring an intensity of a diffraction pattern arising from further aperture positions.

P1059.spec According to a fourth aspect, there is provided a method of imaging a sample, said method comprising: (a) defining a first region of said sample by placing a mask adjacent said sample, wherein an aperture of said mask defines said first region; and (b) exposing said sample to an electromagnetic source; and (c) determining a two-dimensional intensity function at a second region in a plane displaced from said sample; and (d) estimating a two-dimensional phase information of said intensity pattern; and (e) applying a transform to said intensity pattern and said estimated phase pattern, to obtain an estimated sample pattern of said electromagnetic

field within said first region; and

(f) moving said mask relative to said sample, to define a second sample region, said second sample region having a region of partial overlap with I said first sample region; and (g) repeating steps (b) to (f), to obtain a second two-dimensional intensity pattern; and (h) applying a transform to said first intensity pattern and said estimated phase pattern to obtain an estimated first sample pattern; and 3 o (i) applying a transform to said estimated first sample pattern to obtain an estimated second sample pattern of said electromagnetic field within said second region; and P1 059.spec 0) applying a transform to said estimated second sample pattern to obtain an estimated pattern at a region in a plane displaced from said sample; and (k) applying a transform to said estimated pattern at a region in a plane displaced from said sample and said second ho-dimensional intensity pattern to obtain a revised pattern at a region in a plane displaced from said sample; and (I) applying a transform to said revised pattern at a region in a plane displaced from said sample to obtain a revised second sample pattern; and (m) applying a transform to said revised second sample pattern to obtain a revised first sample pattern; and (n) applying a transform to said revised first sample pattern to obtain a revised sample pattern at a second region in a plane displaced from said sample for said first region of said sample; and (0) applying a transform to revised sample pattern at a second region in a plane displaced from sample for a first region of said sample and said first two-dimensional intensity pattern to obtain a revised sample pattern at a second region in a plane displaced from sample for a first region of said sample; and (P) repeating steps (h) to (o) to obtain a refined first sample pattern and a refined second sample pattern.

Preferably, said electromagnetic source comprises a coherent electromagnetic source.

Alternatively, the electromagnetic source comprises an incoherent source.

P1 059.spec Preferably, said mask is placed between said sample and said electromagnetic source.

Alternatively, said mask is placed between said sample and said electromagnetic source.

According to a fifth aspect, there is provided a method for obtaining image data for an object comprising: (a) obtaining a plurality of diffraction patterns from a plurality of aperture positions, each said diffraction pattern corresponding to a known aperture position of said plurality of aperture positions, and; (b) measuring an intensity pattern of each said diffraction pattern; and (c) approximating an exit wave function of said object; and (d) transforming said approximation of said exit wave function of said object using a known aperture transmission function for each said aperture position to obtain a corresponding overall exit wave function for each said aperture position; and (e) transforming each said overall exit wave function, to obtain a corresponding wave function in diffraction space; and (f) modifying each said wave function in diffraction space using said measured intensity patterns at each said aperture position, whilst preserving a phase of each said wave function in diffraction space to obtain a corresponding respective refined wave function in diffraction space for each said aperture position; and P1059.spec (g) transforming each said refined wave function in diffraction space to obtain a corresponding respective refined overall exit wave function for at each aperture position; and (h) obtaining a corresponding respective value of said exit wave function for each said aperture position; and (i) obtaining an average value of said exit wave function from said plurality of values of said exit wave function; and (j) repeating (d) to (h) to obtain a refined exit wave function of said object.

Preferably, said transformation of step (e) comprises a Fourier transformation; and said transformation of step (g) comprises an inverse Fourier transformation.

Preferably, said transformation of step (h) is not performed where said 2 0 aperture transmission function of said aperture approaches zero.

Preferably, said average value in step (I) comprises a mean.

Preferably, said mean is weighted by a modulus of each said aperture 2 5 transmission function at each aperture position.

According to a sixth aspect, there is provided an algorithm comprising: I (a) transforming a first function (ok) to a second function 6(r); and (b) transforming said (or) to a third function;2(r); and P1 059.spec (c) transforming said 62(r) to a fourth function 2(k); and (d) modifying said I2(k) to make it consistent with a known fifth function 12 (k)| ; and (e) transforming said modified I2(k) to a revised third function ó2(r); and (f) transforming said revised;2(r) to a revised second function 6(r); o and (g) transforming said revised (I) to a revised first function I it and (h) modifying said I(k) to make it consistent with a known sixth function | (k)| 2 (i) repeating steps (a) to (h) to obtain refined values for (I) and ó2(r); wherein, 6(r), i2(r), I(k), I2(k) represent complex functions, ,(k) represents the square of the modulus of I(k) and |2(k)| represents the square of the modulus of 2(k).

Preferably, said algorithm is used to obtain a refined value for 6(r) and a refined value for i2(r).

Preferably, said algorithm is used to construct image data.

P1059.spec Preferably, said transformation in step (a) comprises an inverse Fourier transformation; and said transformation in step (c) comprises a Fourier transformation; and said transformation in step (e) comprises an inverse Fourier transformation; and said transformation in step (g) comprises a Fourier transformation.

Preferably, said modification of 92(k) in step (d) preserves a phase of I2(k); and said modification of (ok) in step (h) preserves a phase of Ii(k).

Preferably, said transformation in step (c) comprises dividing by a first complex function, and multiplying by a second complex function; and ignoring values for ó2(r) where said first complex function is substantially zero.

Preferably, said transformation in step (d) comprises dividing by a second complex function, and multiplying by a first complex function; and ignoring values for 6(r) where said second complex function is substantially zero.

Preferably, Ink) represents a wave function of radiation in diffraction 3 o space where a aperture is in a first position; and P1059.spec 2(k) represents a wave function of radiation in diffraction space where a aperture is in a second position; and (I) represents an exit wave function of radiation where said aperture is in said first position; and 6(r) represents an exit wave function of radiation where said aperture is in second position; and lo | (k)| represents an intensity of (I); and 12 (k)| represents an intensity of I (k).

According to a seventh aspect, there is provided a computer program comprising program instructions for causing a computer to form the process of any preceding claims.

Preferably, said computer program is stored on a data carrier.

According to an eighth aspect, there is provided apparatus for obtaining image data for an object comprising: a radiation source; and s a holder, configured to locate said object to be imaged; and an aperture; and means to moveably position said aperture relative to said object in at least a 3 o first position and a second position; and P1059.spec a detector, configured to detect an intensity of a far-field diffraction pattern arising from an interaction between said radiation and said object; and means to process said intensity data.

Preferably, said means to detect an intensity of radiation comprises a CCD detector.

To Preferably, said radiation source comprises a coherent radiation source.

Alternatively, said radiation source comprises an incoherent radiation source.

Preferably, said object is located between said radiation source and said aperture.

Alternatively, said aperture is located between said radiation source and said object to be imaged.

Preferably, said means to move said aperture comprises a micro-actuator.

Preferably, said means to process said intensity data comprises: s a microprocessor; and a data carrier comprising instructions for said microprocessor to perform an analysis of said data; and 3 o a data input device configured to allow a user to input instructions; and P1 059.spec means to instruct a movement of said aperture via said aperture movement means.

Preferably, the apparatus further comprises at least one lens located between said aperture and said detector, said lens configured to alter a camera length of said apparatus.

Preferably, the apparatus further comprises at least one lens located between said object and said radiation source.

According to a ninth aspect, there is provided apparatus for constructing image data for a region of an object comprising: means to analyze an intensity data of a diffraction pattern arising from said s region, said intensity data arising from a function of a known aperture, wherein said aperture can be moved to at least two different positions relative to said object.

According to a tenth aspect, there is provided apparatus for obtaining image o data for an object comprising: (i) means to obtain a first diffraction pattern of said object where an aperture is in a first position; and (ii) means to obtain a second diffraction pattern of said object where said aperture is in a second position; and (iii) means to measure an intensity of said first diffraction pattern; and (iv) means tomeasure an intensity of said second diffraction pattern; and P1059.spec (v) means to approximate a phase of said first diffraction pattern; and (vi) means to combine said phase and said measured intensity of said first diffraction pattern to form a wave function of said first diffraction pattern; and (vii) means to transform said wave function of said first diffraction pattern to obtain an estimate of a wave function of said object where said aperture is in a first position; and (viii) means to transform said estimate of said wave function for said object where said aperture is in said first position to an estimate of a wave function for said object where said aperture is in said second position; and (ix) means to transform said wave function of said object where said :5 aperture is in said second position to obtain an estimate of said wave function of said diffraction pattern where said aperture is in said second position; and (x) means to modify said wave function of said diffraction pattern when said aperture is in said second position using said measured intensity of said So second diffraction pattern; and According to an eleventh aspect, there is provided apparatus for obtaining image data for an object comprising: (a) means to obtain a plurality of diffraction patterns from a plurality of aperture positions, each said diffraction pattern corresponding to a known aperture position of said plurality of aperture positions, and; (b) means to measure an intensity pattern of each said diffraction So pattern; and (c) means to approximate an exit wave function of said object; and P1 059. spec (d) means to transform said approximation of said exit wave function of said object using a known aperture transmission function for each said aperture position to obtain a corresponding overall exit wave function for each said aperture position; and (e) means to transform each said overall exit wave function, to obtain a corresponding wave function in diffraction space; and 0 (f) means to modify each said wave function in diffraction space using said measured intensity patterns at each said aperture position, whilst preserving a phase of each said wave function in diffraction space to obtain a corresponding respective refined wave function in diffraction space for each said aperture position; and (g) means to transform each said refined wave function in diffraction space to obtain a corresponding respective refined overall exit wave function for at each aperture position; and (h) means to obtain a corresponding respective value of said exit wave function for each said aperture position; and (i) obtaining an average value of said exit wave function from said plurality of values of said exit wave function; and (i) repeating (d) to (h) to obtain a refined exit wave function of said object.

Brief Description of the Drawinus

For a better understanding of the invention and to show how the same may be carried into effect, there will now be described by way of example only, specific embodiments, methods and processes according to the present invention with reference to the accompanying drawings in which: P1059.spec Figure 1 illustrates schematically the prior art problem of achieving a low value for d.

Figure 2 illustrates schematically prior art Gabor holography.

Figure 3 illustrates schematically a prior art technique for obtaining information about the imaged object from a far-field diffraction pattern.

Figure 4 illustrates schematically the prior art Fienup process for obtaining a wave function of radiation.

Figure 5 illustrates schematically a process for obtaining a far-field diffraction pattern.

Figure 6 illustrates schematically an alternative arrangement for obtaining a far-field diffraction pattern where the aperture is located below the object.

Figure 7 illustrates schematically an algorithm for obtaining a wave function 2 o of an object.

Figure 8 illustrates schematically a process of obtaining an exit wave function of an object.

Figure 9 illustrates schematically an alternative process of obtaining an exit wave function of an object.

Figure 10 illustrates schematically apparatus for far-field imaging of an object.

Detailed Description

P 1 059.spec There will now be described by way of example a specific mode contemplated by the inventors. In the following description numerous specific details are set forth in order to provide a thorough understanding. It will be apparent however, to one skilled in the art, that the present invention may be practiced without limitation to these specific details. In other instances, well known methods and structures have not been described in detail so as not to

unnecessarily obscure the description.

Terms and definitions The term radiation denotes energy from a source, and includes electromagnetic radiation, emitted particles such as electrons, and acoustic waves. Radiation can be represented by a wave function.

A wave function comprises a real part and an imaginary part. It can be represented by its modulus and phase. 6(r)* is the complex conjugate of ó(r), and;(r) \6(r)* = |Y7(r)|, where |y'(r)| is an intensity of the wave function.

The modulus of the wave function is determined from the square root of the intensity.

go The term far-field is used to denote a region which is a relatively long distance from a wave function of interest.

Diffraction space is also known as Fourier space.

The term aperture is used to describe a localized transmission function of radiation that can be represented by a complex variable in two dimensions having a modulus value between O and 1, for example an aperture in a mask or a region where an electron beam is brought substantially to a focus.

O(r) is an exit wave function of radiation after interaction with an object. If an aperture is displaced some distance away from the exit of the object, this P1 059 spec function may have undergone Fresnel propagation to the plane of the aperture.

It can be represented as a complex function.

P(r - Rim) is an aperture transmission function where an aperture is in a first position, and can be represented as a complex function. Its complex value is given by modulus and phase alterations it introduces to a perfect plane wave incident upon it.

P(r- R2) is an aperture transmission function where an aperture is in a To second position, and can be represented as a complex function Its complex value is given by modulus and phase alterations it introduces to a perfect plane wave incident upon it.

The aperture transmission function may be different for each different aperture position relative to the object.

((r) is an exit wave function of radiation is it exits the aperture and the object where an aperture is in a first position.

ó2(r) is an exit wave function of radiation is it exits the aperture and the object where an aperture is in a second position.

I (k) is a wave function of radiation in diffraction space where the aperture is in a first position.

92(k) is a wave function of radiation in diffraction space where the aperture is in a second position.

P1059.spec |W, (k)| is the square of the modulus of a wave function of the radiation in diffraction space where the aperture is in a first position, and is measured as an intensity of a measured diffraction pattern.

12 (k)| iS the square of the modulus of a wave function of the radiation in diffraction space where the aperture is in a second position, and is measured as an intensity of a measured diffraction pattern.

k is a vector co-ordinate in diffraction space.

r is a vector co-ordinate in real space.

Rat and R2 are vector co-ordinates representing positions to which an aperture is shifted in real space in a first position and a second position.

Referring to figure 5 herein, there is illustrated schematically a process for obtaining a far-field diffraction pattern. A radiation source 501 is used to produce a beam 502 of radiation. The beam 502 passes through an aperture 503.

Interaction between the beam 502 and the aperture 503, such as Fresnel 2 0 diffraction, propagates the beam 502 which then has a complex aperture transmission function P(r - Rat) 504. The propagated beam passes through an object 505, where further interactions with the specimen further alter the wave function of the beam 506. The altered wave function V(r) 506 is a complex wave function.

The resultant diffracted radiation forms a diffraction pattern in the farfield 507, the intensity of which can be measured.

Referring to Fig. 6 herein there is illustrated schematically an alternative So arrangement for obtaining a far-field diffraction pattern where the aperture is P1 059.spec located below the object. In this instance, a first interaction of the radiation 502 is with the object 503, which forms a complex wave function 0 (r) 601.

For both the arrangements described above, the resultant complex wave function 506 is related to O(r) and P(r - Rat) by equation 2.

ó(r) = 0(r) P(r - Rat) (2) If P(r - Rim) is known, and ó(r) can be found then O(r) can be determined, thereby providing image data relating to the object.

An intensity of an electron diffraction pattern is measured where an aperture is positioned relative to an object to be imaged in a first position (position 1). An intensity of an electron diffraction pattern is then measured where an aperture is positioned relative to an object to be imaged in a second position (position 2).

From these measurements, and from the known aperture positions, it is possible to work out a wave function for the object that is to be imaged, and therefore to obtain image data relating to the object.

2 o There are many of techniques that can be used to find;(r) using measured diffraction pattern intensities, and it will be appreciated that any of these may be employed. The following examples illustrate techniques that can be used.

Example 1

Referring to figure 7 herein, there is illustrated schematically an algorithm for obtaining a wave function of an object. A measured intensity of the diffraction pattern where the aperture is in the first position | (k)| 701 forms the basis of an estimate of the complex wave function of the diffraction pattern. However, as | (k)| is an intensity value, it does not give information about the phase of the 3 o wave function in diffraction space. Therefore, an estimate of the phase is made, P1 059.spec and combined 702 with the square root of the measured intensity 701 to give an estimate of the wave function of the radiation in diffraction space I(k) 703 where the aperture is in position 1. The estimate of the phase may be at random.

An inverse Fourier transformation 704 is performed on I (k) 703 to obtain an estimate of the exit wave function of the radiation as it exits the aperture and the object ó(r) 705 where the aperture is in position 1.

(or) is a product of the wave function of the radiation as it exits the object Jo O(r) and the aperture transmission function P(r- Ret) where the aperture is in position 1 (equation 2).

Similarly, it is known that ó2(r) is a product of the wave function of the radiation as it exits the object O(r) and the wave function of the radiation as it exits the aperture (P(r - R2)) where the aperture is in position 2. This is expressed as: \6 2(r) = 0(r)P(r - R2) (3) It is therefore possible to transform 706 ó(r) 705 to obtain the exit wave function of the radiation as it exits the aperture and the object 62(r) 707 where the aperture is in position to using the equation 4: p( '/ ) x P(r - R2) = 772 (r) (4) A Fourier transformation 708 is performed on ó2(r) 707 to give an estimate of the wave function of the radiation in diffraction space I2(k) 709 where the aperture is in position 2. The intensity of this diffraction pattern has been P1 059.spec measured |2(k)| 711. |2(k)| 711 is used to correct the estimated wave function I2(k) 709. However, in this correction the phase component I2(k) 709 is preserved.

An inverse Fourier transformation 712 is performed on the corrected diffraction pattern wave function I2(k) 709 to obtain a new estimate of 62(r) 707.

62(r) is transformed 713 using a similar equation to equation 4 to obtain a revised estimate of 6(r) 705. A Fourier transformation 714 is then performed on i o {(r) 705 to obtain a revised estimate of I (k) 703.

Measured intensity data of the diffraction pattern | (k)| 701, where the aperture is in position 1, is used to correct the revised wave function (ok) 703, whilst preserving the phase component of I (k) 703.

The above process of steps 704, 706, 708, 710, 712, 713, and 714 are iterated to obtain refined exit wave functions ((r) 705 and ó2(r) 707.

The refined wave functions;(r) 705 and ó2(r) 707 can be related to the 2 0 exit wave function of the object using known P(r - R2) and P(r - Rim), to obtain an exit wave function O(r) of radiation after interaction with an object. From O(r), image data relating to the structure of the object can be obtained.

As I(k) 803 and I2(k) 809 are updated with measured intensity data from the diffraction patterns (|! (k)| ) 801 and (|Y'2 (k)| ) 811, the revised estimates of V(r) 805 and 62(r) improve with each iteration of the process.

P1 059.spec Referring to figure 8 herein, there is illustrated schematically a process of obtaining an exit wave function of an object. The image of the dog 801 represents the modulus component of an exit wave function O(r), and the image of the bird 802 represents a phase component of a object wave function O(r).

These images 801, 802 represent the information that is required to obtain an image of the object.

A first aperture position 803 and a second aperture position 804 are shown here as circles for the purposes of illustration only. In most circumstances, an Jo aperture transmission function would comprise a complex wave function.

When the aperture is in position 1, the exit wave function ó(r) comprises a modulus component 805 and a phase component 806.

The wave function in diffraction space I(k) where the aperture is in position 1 also comprises a diffraction pattern intensity 807 and phase information 808. In practice, the diffraction pattern intensity 807 is all that can be measured. For clarity, the diffraction pattern intensity is not shown to scale in this illustration.

By measuring the diffraction pattern intensity at a first aperture position and a diffraction pattern intensity at a second aperture position, and estimating a phase of the exit wave function 6(r), the object exit wave function intensity 801 and phase 802 can be reconstructed to give an object intensity 809 where the aperture is in position 1 and position 2, and an object phase where the aperture is in position 1 and position 2.

The transformation of (or) to 6(r) is given by equation 4. However, many values of P(r - Rim) will approach zero, therefore giving meaningless data for (or), as the aperture only covers a certain area of the object. The P1 059.spec transformation shown in equation 4 is therefore only performed where P(r - Rim) is significantly greater than zero. Similarly, the transformation of 62(r) to V(r) is only performed where P(r - R2) is significantly greater than zero. The transformation given by equation 4 is therefore only performed where meaningful data can be obtained. It has been found that the transformation of equation 4 is ideally performed where values of the aperture transmission function are at least 10% of their maximum value.

Ideally, there is overlap between the first aperture position 803 and the second aperture position 804. The intensity portion of the object 809 and the phase portion of the object 810 can only be obtained for the first and second aperture position.

It will be appreciated that this technique is not limited to two aperture positions. Third and further aperture positions may also be introduced to obtain image data for a larger object area, and to improve the accuracy of the revised values for ó(r) and;2(r) The above example to determine O(r) requires using known P(r - R2) and P(r - Rim). P(r - R2) and P(r - Ret) are found experimentally.

The above example also requires making an estimate of a wave function, or a phase component of a wave function. In the example given, an estimate is made of the phase of (ok) 703. It will be appreciated that the estimate is 2 5 required to provide an estimated wave function that is then refined by the iterative algorithm shown in figure 7. The estimate of the phase of (ok) 703 is made to provide a wave function that can then be used to obtain refined O(r). However, the estimate need not be of a phase of I (k) 703. An estimate could be made of a phase of I2(k) 709, and combined 710 with the square root of the measured P1 059.spec intensity 711 to provide an estimate of I2(k) 709. Similarly, an estimate could be made of (or) 705 or ó2(r) 707 and used as a starting point for the algorithm.

Example 2

An aperture is positioned relative to an object to be imaged in several positions. In this example, an aperture is positioned relative to the object in a first, a second, a third, a fourth and a fifth position, although it will be appreciated that any number of aperture positions greater than two may be used. Some overlap is required between the aperture positions. An intensity of a JO corresponding respective diffraction pattern is then measured for each aperture position. From these measurements, and from the known aperture positions, it is possible to work out a wave function for the object that is to be imaged, and therefore to obtain image data relating to the object.

Referring to figure 9 herein, there is illustrated schematically an alternative process of obtaining an exit wave function of an object. An estimate is made of an exit wave function of an object O(r) 901. This estimate of O(r) 901 is multiplied 902, 903, 904, 905, 906 by an aperture transmission function at each aperture position to obtain estimates for the exit wave function at each aperture position, ó(r) 907, ó2(r) 908, 63(r) 909, 64(r) 910, and ó5(r) 911.

A Fourier transform is applied 912, 913, 914, 915, 916 to each exit wave function (or) 907, ó2(r) 908, 63(r) 909, ;4(r) 910, and ó5(r) 911. This gives estimated wave functions in diffraction space for each aperture position (ok) 917, 92(k) 918, I3(k) 919, I4(k) 920, and I(k) 921.

Intensity measurements | (k)| 922, 12 (k)l 923, 13 (k)l 924' 14 (k)| 925, and As (k)| 925 of electron diffraction pattern have been measured for each aperture position. These are used to refine 927, 928, 929, P1059.spec 930, 931 estimated values I,(k) 917, 2(k) 918, I3(k) 919, 4(k) 920, and Ii(k) 921, whilst preserving a phase component of each of I(k) 917, I2(k) 918, I3(k) 919, 4(k) 920, and j(k) 921.

A Fourier transform is applied 932, 933, 934, 935, 936 to the refined values of values 9(k) 917, I2(k) 918, I3(k) 919, I4(k) 920, and (ok) 921. This gives refined values for each exit wave function (I) 907, J'2(r) 908, 63(r) 909, 64(r) 91 O. and 65(r) 911 at each aperture position.

JO Using known aperture transmission functions at each aperture position, the exit wave functions (I) 907, ó2(r) 908, ó3(r) 909, 64(r) 910, and yJS(r) 911 can be transformed 937, 938, 939, 940, 941 to give refined values for O(r) 901.

Many values for each aperture transmission function will approach zero, as the aperture only covers a certain area of the object. The transformations 937, 938, 939, 940, 941 are only made for each aperture transmission function where their values are significantly greater than zero. The values of O(r) 901 can then be combined as a mean, or a mean weighted by a modulus of the aperture transmission function at each aperture position, to obtain a refined estimate of O(r). Further iterations proceed using the refined estimate of O(r).

By repeating the above process, refined values for O(r) 901, and hence image data relating to the structure of the object can be obtained. An area of image data obtained by this method is an area spanned by a union of all aperture position areas. The aperture positions will in certain cases overlap with each other, and a greater degree of overlap will improve a convergence of the algorithm for estimating O(r) because more independent measurements of intensity of each diffraction pattern of the object at different aperture positions provide more information.

P1 059.spec ln example 2, the estimate of the wave function O(r) is made for convenience. However, an estimated wave function may be made for any of the wave functions as a starting point for the algorithm. For example, an estimated phase can be made for of each of (ok) 917, I2(k) 918, I3(k) 919, I4(k) 920, and (ok) 921.

Apparatus Referring to figure 10 herein, there is illustrated schematically apparatus for far-field imaging of an object. The apparatus comprises a radiation source 1001, configured to emit radiation 1002. The radiation 1002 interacts with an object to be imaged 903 to give an object wave function 1004. The radiation then passes through an aperture 1005. Interactions between the radiation 1002 and the aperture 1005 further modify the radiation to give a complex exit wave function 16(r) 1006. The position of the aperture 1005 can be altered with respect to the position of the object 1003 using an actuator 1007. In this way the aperture 1005 is positioned in a first position, and then moved to a second position. The aperture can be moved to further positions. The actuator 1007 comprises a piezoelectric actuator capable of moving at Angstrom resolution over a field of up to 1,um.

The diffracted electron beam 1008 forms a diffraction pattern in the farfield space, the intensity of which can be measured using a CCD detector 1009. By moving the aperture 1005 using the actuator 1007, diffraction pattern intensities can be measured using the CCD detector 1009 where the aperture 1005 is in a 2 5 first position, a second position, and if desired further positions.

The size of the CCD detector array required relates to the size of the aperture. As the aperture size is reduced, a size of allowed features in the far field diffraction pattern increase. It has been determined that a CCD array of 3 o 2000 x 2000 pixels corresponds to a resolution of around 1/2000th of the aperture size. Using an aperture size of 50 A gives an estimated resolution of 0.25 A, P1 059.spec compared to a resolution in a conventional transmission electron microscope of around 2 A. A control unit 1010 is used to control the position of the aperture 1005 and to process the diffraction pattern intensity data obtained from the CCD detector 1 009.

The control unit 1010 comprises a microprocessor 1011, a memory 1012, a data storage device 1013, a display 1014, a data inputting device 1015, and a To device 1016 for receiving data from the CCD detector 1009 and transmitting data to control the actuator 1007.

The data input device 1015 is used to instruct the microprocessor 1011 to move the aperture 1005 to a known first position. Once the aperture 1005 is at the first position, the object of the image 1003 is subjected to radiation 1002, and an intensity of a first diffraction pattern is obtained using the CCD detector 1009.

The intensity data of the first diffraction pattern is stored in the memory 1012.

The aperture 1005 is then moved to a second position using the actuator 1007, controlled by the microprocessor 1011. The object to be imaged 1003 is then subjected to radiation 1002, and a second diffraction pattern intensity is measured using the CCD detector 1009. The second diffraction pattern intensity data is stored in the memory 1012.

The microprocessor 1011 processes the first diffraction pattern intensity data and the second diffraction pattern intensity data using instructions stored in the data storage 1013 to obtain an exit wave function O(r) of radiation after interaction with the object 1005. The exit wave function can be used to obtain image data relating to the object 1005 P1059 spec The radiation source 1001 comprises a coherent radiation source. The radiation source 1001 also produces substantially monochromatic electromagnetic radiation.

In an second alternative arrangement, the aperture 1005 is positioned above the object to be imaged 1003, such that the radiation 1002 passes through the aperture 1005 before it interacts with the object to be imaged 1003.

In a third alternative arrangement, the radiation source comprises an 0 incoherent red iation sou roe.

In a further alternative arrangement, the radiation 1002 is not transmitted through the object 1003. The radiation 1002 interacts with the object of the image 1003 such that the object emits other forms of radiation that can form diffraction patterns in the far-field. For example, the object may be subjected to x-ray radiation, and emit photoelectrons. The photoelectrons form a diffraction pattern in the farfield, the intensity of which can be measured to provide data relating to the object.

In a further alternative arrangement, an electron lens is mounted after the object 1003 and the aperture 1005 to alter a camera length of the apparatus for

far-field imaging of an object.

In a further alternative arrangement, an electron lens is mounted between the radiation source 1001 and the object 1003 to condense the radiation onto the region of the object to be imaged.

P1 059.spec

Claims

Claims: 1. A method of constructing image data for a region of an object

comprising: analyzing an intensity data of a diffraction pattern arising from said region, said intensity data arising from a function of a known aperture, wherein said aperture can be moved to at least two different positions relative to said object.
2. A method of constructing image data for a region of an object as JO claimed in any one of claim 1 wherein said intensity data of said diffraction pattern is measured in a far-field of an electron microscope.
3. A method of constructing image data for a region of an object as claimed in claim 1 or claim 2 wherein said analysis comprises at least one Fourier transformation.
4. A method of constructing image data for a region of an object as claimed in any one of claims 1 to 3 wherein said analysis is an iterative process.
5. A method of constructing image data for a region of an object as claimed in any one of claims 1 to 4 wherein said analysis comprises estimating a wave function.
6. A method of constructing image data for a region of an object as claimed in any one of claims 1 to 5 wherein said analysis comprises only using data where a value for an aperture transmission is substantially greater than zero.
7. A method of constructing image data for a region of an object as claimed in claims 5 or claim 6 wherein an estimated phase of said diffraction pattern is combined with said intensity data of said diffraction pattern to form an estimate of a wave function of said diffraction pattern.

P1059.spec
8. A method of constructing image data for a region of an object as claimed in claim 7 wherein said analysis comprises transforming said estimate of said wave function of said diffraction pattern to obtain an estimate of a wave function of said region of said object.
9. A method of constructing image data for a region of an object as claimed in claims 5 or claim 6 wherein an exit wave function of said region of an object is estimated.

To
10. A method of constructing image data for a region of an object as claimed in claim 9 wherein said analysis comprises transforming said estimated exit wave function of said object using a known aperture transmission function.
11. A method of constructing image data for a region of an object as claimed in any preceding claim wherein said analysis comprises: correcting a wave function of said diffraction pattern using said intensity data of said diffraction pattern; and 2 o preserving a phase of said wave function of said diffraction pattern.
12. A method of constructing image data for a region of an object as claimed in any preceding claim wherein said diffraction pattern arises from interaction of radiation from a radiation source with said object.
13. A method for obtaining image data for an object comprising: (i) obtaining a first diffraction pattern of said object where an aperture is in a first position; and (ii) obtaining a second diffraction pattern of said object where said aperture is in a second position; and P1059.spec (iii) measuring an intensity of said first diffraction pattern; and (iv) measuring an intensity of said second diffraction pattern; and (v) approximating a phase of said first diffraction pattern; and (vi) combining said phase and said measured intensity of said first diffraction pattern to form a wave function of said first diffraction pattern; and (vii) transforming said wave function of said first diffraction pattern to obtain an estimate of a wave function of said object where said aperture is in a first position; and (viii) transforming said estimate of said wave function for said object where said aperture is in said first position to an estimate of a wave function for said object where said aperture is in said second position; and (ix) transforming said wave function of said object where said aperture is in said second position to obtain an estimate of said wave function of said diffraction pattern where said aperture is in said second position; and (x) modifying said wave function of said diffraction pattern when said aperture is in said second position using said measured intensity of said second diffraction pattern; and
14. A method for obtaining image data as claimed in claim 13, further comprising: 3 o (a) performing the inverse operation of step (ix); and P1059.spec (b) transforming a new estimate of said wave function for said object where said aperture is in said second position to a new estimate of a wave function for said object where said aperture is in said first position; and (c) performing an inverse operation of (vii); and (d) modifying a new estimate of a wave function of said diffraction pattern where said aperture is in said first position using said measured intensity of said first diffraction pattern; and (e) repeating steps (vii) to (x) and steps (a) to (d) to obtain a refined wave function of said object where said aperture is in a first position, and a refined wave function of said object where said aperture is in a second position.
15. A method for obtaining image data as claimed in claim 13 or claim 14 wherein said transformations of steps (ix) and (c) comprise a Fourier transformation.
16. A method for obtaining image data as claimed in any one of claims go 13 to 15 wherein said transformations of steps (vii) and (a) comprise an inverse Fourier transformation.
17. A method for obtaining image data as claimed in any one of claims 13 to 16 wherein said transformation of steps (viii) and (b) comprises dividing an estimate of a wave function for said object by an aperture transmission function of said aperture.
18. A method for obtaining image data as claimed in claim 17 wherein said division is not performed where said aperture transmission function of said 3 o aperture approaches zero.

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19. A method as claimed in any one of claims 17 or 18 wherein said aperture transmission function of said aperture comprises complex data.
20. A method as claimed in any one of claims 13 to 18 wherein said diffraction patterns are obtained where said aperture is in more than two positions.
21. A method for obtaining image data for an object as claimed in any preceding claim wherein said phase of said first diffraction pattern is preserved during step (d).
22. A method for obtaining image data for an object as claimed in any one of claims 13 to 21 wherein said phase of said second diffraction pattern is preserved during step (x).
23. A method of constructing image data comprising: (a) measuring an intensity of a first diffraction pattern arising from a first aperture position; and (b) measuring an intensity of a second diffraction pattern arising from a second aperture position; and (c) estimating a phase of said first diffraction pattern; and (d) combining said estimate of said phase with said intensity Is measurement of said first diffraction pattern to form a wave function of said first diffraction pattern; and 3 o (e) transforming said first diffraction pattern wave function to obtain an estimate of a wave function of an object; and P1059.spec (f) updating said estimate of said wave function of said object using a first known aperture position; (g) determining a wave function of said object at said second aperture position; (h) transforming said second object wave function to obtain an estimated wave function of said second diffraction pattern; and To (i) comparing said estimated wave function of said second diffraction pattern with said measured second diffraction pattern; and 0) altering an intensity component of said estimated wave function of said second diffraction pattern, to match said measured intensity of said second diffraction pattern, whilst preserving a phase component of said estimated wave function of said second diffraction pattern, to obtain a revised estimate of said second wave function of said second diffraction pattern; and (k) transforming said second revised estimate of said wave function of 2 0 said second diffraction pattern, to obtain a revised wave function of said object at said second aperture position; and (1) determining a revised wave function of said object at said first aperture position; and (m) transforming said revised wave function of said object at said first aperture position, to obtain a revised wave function of said first diffraction pattern; and (n) altering an intensity component of said revised wave function of said first diffraction pattern, to match said measured intensity of said first diffraction pattern, whilst preserving a phase component of said revised wave P1059.spec function of said first diffraction pattern, to obtain a modified wave function of said first diffraction pattern; and (o) repeating steps (e) to (n) to obtain a refined wave function of said object at said first aperture position and a refined wave function of said object at said second aperture position.
24. A method of constructing image data as claimed in claim 23, wherein said transformation of steps (e) and (k) is an inverse Fourier o transformation.
25. A method of constructing image data as claimed in claim 23 or claim 24 wherein said transformation of steps (h) and (m) is a Fourier transformation.
26. A method for obtaining image data as claimed in any one of claims 23 to 25 wherein said transformation of steps (g) and (I) comprises dividing an estimate of a wave function for said object by an aperture transmission function of said aperture.
27. A method of constructing image data as claimed in claim 26 wherein said division is not performed where said aperture transmission function of said aperture approaches zero.

z
28. A method as claimed in any one of claims 23 to 27 wherein said aperture transmission function of said aperture comprises a complex wave function.
29. A method of constructing image data as claimed in any one of claims 23 to 28 further comprising measuring an intensity of a diffraction pattern arising from further aperture positions.

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30. A method of imaging a sample, said method comprising: (a) defining a first region of said sample by placing a mask adjacent said sample, wherein an aperture of said mask defines said first region; and (b) exposing said sample to an electromagnetic source; and (c) determining a two-dimensional intensity function at a second region in a plane displaced from said sample; and (d) estimating a two-dimensional phase information of said intensity pattern; and (e) applying a transform to said intensity pattern and said estimated phase pattern, to obtain an estimated sample pattern of said electromagnetic

field within said first region; and

(f) moving said mask relative to said sample, to define a second sample region, said second sample region having a region of partial overlap with 2 o said first sample region; and (g) repeating steps (b) to (f), to obtain a second two-dimensional intensity pattern; and 2 5 (h) applying a transform to said first intensity pattern and said estimated phase pattern to obtain an estimated first sample pattern; and (i) applying a transform to said estimated first sample pattern to obtain an estimated second sample pattern of said electromagnetic field within said o second region; and P1 059.spec (j) applying a transform to said estimated second sample pattern to obtain an estimated pattern at a region in a plane displaced from said sample; and (k) applying a transform to said estimated pattern at a region in a plane displaced from said sample and said second two-dimensional intensity pattern to obtain a revised pattern at a region in a plane displaced from said sample; and (I) applying a transform to said revised pattern at a region in a plane To displaced from said sample to obtain a revised second sample pattern; and (m) applying a transform to said revised second sample pattern to obtain a revised first sample pattern; and (n) applying a transform to said revised first sample pattern to obtain a revised sample pattern at a second region in a plane displaced from said sample for said first region of said sample; and (o) applying a transform to revised sample pattern at a second region go in a plane displaced from sample for a first region of said sample and said first two-dimensional intensity pattern to obtain a revised sample pattern at a second region in a plane displaced from sample for a first region of said sample; and (p) repeating steps (h) to (o) to obtain a refined first sample pattern and s a refined second sample pattern.
31. The method as claimed in claim 30, wherein said electromagnetic source comprises a coherent electromagnetic source.

So
32. The method as claimed in claim 30, wherein said electromagnetic source comprises an incoherent source.

P1 059.spec
33. The method as claimed in any one of claims 30 to 32, wherein said mask is placed between said sample and said electromagnetic source.
34. The method as claimed in any one of claims 30 to 32, wherein said mask is placed between said sample and said electromagnetic source.
35. A method for obtaining image data for an object comprising: (a) obtaining a plurality of diffraction patterns from a plurality of aperture positions, each said diffraction pattern corresponding to a known aperture position of said plurality of aperture positions, and; (i) measuring an intensity pattern of each said diffraction pattern; and (i) approximating an exit wave function of said object; and (k) transforming said approximation of said exit wave function of said object using a known aperture transmission function for each said aperture position to obtain a corresponding overall exit wave function for each said aperture position; and (1) transforming each said overall exit wave function, to obtain a corresponding wave function in diffraction space; and (m) modifying each said wave function in diffraction space using said measured intensity patterns at each said aperture position, whilst preserving a phase of each said wave function in diffraction space to obtain a corresponding respective refined wave function in diffraction space for each said aperture position; and P1 059.spec (n) transforming each said refined wave function in diffraction space to obtain a corresponding respective refined overall exit wave function for at each aperture position; and (0) obtaining a corresponding respective value of said exit wave function for each said aperture position; and (i) obtaining an average value of said exit wave function from said plurality of values of said exit wave function; and (j) repeating (d) to (h) to obtain a refined exit wave function of said object.
36. A method of obtaining image data as claimed in claim 35 wherein said transformation of step (e) comprises a Fourier transformation; and said transformation of step (g) comprises an inverse Fourier transformation.
37. A method as claimed in claim 35 or claim 36 wherein said transformation of step (h) is not performed where said aperture transmission function of said aperture approaches zero.
38. A method as claimed in any one of claims 35 to 37 wherein said average value in step (1) comprises a mean.
39. A method as claimed in claim 38 wherein said mean is weighted by a modulus of each said aperture transmission function at each aperture position.
40. An algorithm comprising: (i) transforming a first function I(k) to a second function;(r); and P1 059.spec 0) transforming said;(r) to a third function ó2(r); and (k) transforming said 62(r) to a fourth function I2(k); and (1) modifying said I2(k) to make it consistent with a known fifth function |Y'2 (k)| ; and (m) transforming said modified 92(k) to a revised third function ó2(r); and (n) transforming said revised ó2(r) to a revised second function ó(r); and (o) transforming said revised 6(r) to a revised first function I ok); and (p) modifying said I(k) to make it consistent with a known sixth function |1'(k)| (i) repeating steps (a) to (h) to obtain refined values for 6(r) and 2 0 ó2(r); wherein, ó(r), ó2(r), I(k), I2(k) represent complex functions, |(k) | represents the square of the modulus of +(k) and |2(k)| represents the square of the modulus of I2(k).
41. An algorithm as claimed in claim 40, wherein said algorithm is used to obtain a refined value for 6(r) and a refined value for 62(r).

P1 059.spec
42. An algorithm as claimed in claim 40 or claim 41, wherein said algorithm is used to construct image data.
43. An algorithm as claimed in any one of claims 40 to 42, wherein: said transformation in step (a) comprises an inverse Fourier transformation; and To said transformation in step (c) comprises a Fourier transformation; and said transformation in step (e) comprises an inverse Fourier transformation; and said transformation in step (g) comprises a Fourier transformation.
44. An algorithm as claimed in any one of claims 40 to 43 wherein said modification of I2(k) in step (d) preserves a phase of I2(k); and 2 0 said modification of I t(k) in step (h) preserves a phase of (k).
45. An algorithm as claimed in any one of claims 40 to 44 wherein said transformation in step (c) comprises dividing by a first complex function, and multiplying by a second complex function; and ignoring values for; 2(r) where said first complex function is substantially zero.
46. An algorithm as claimed in any one of claims 40 to 46 wherein said transformation in step (d) comprises dividing by a second complex function, and multiplying by a first complex function; and P1 059.spec ignoring values for ó (r) where said second complex function is substantially zero.
47. An algorithm as claimed in any one of claims 40 to 46 wherein: (I) represents a wave function of radiation in diffraction space where a aperture is in a first position; and 12(k) represents a wave function of radiation in diffraction space where a aperture is in a second position; and 6(r) represents an exit wave function of radiation where said aperture is in said first position; and 62(r) represents an exit wave function of radiation where said aperture is in second position; and | (k)| represents an intensity of I j(k); and 12 (k)| represents an intensity of I(k).
48. A computer program comprising program instructions for causing a computer to form the process of any one of the preceding claims.
49. A computer program as claimed in claim 48, stored on a data carrier.
50. Apparatus for obtaining image data for an object comprising: P1 059. spec a radiation source; and a holder, configured to locate said object to be imaged; and an aperture; and means to moveably position said aperture relative to said object in at least a first position and a second position; and a detector, configured to detect an intensity of a far-field diffraction pattern arising from an interaction between said radiation and said object; and means to process said intensity data.
51. Apparatus for obtaining image data for an object as claimed in claim 50 wherein said means to detect an intensity of radiation comprises a COD detector.
52. Apparatus for obtaining image data for an object as claimed in 2 0 claim 50 or claim 51 wherein said radiation source comprises a coherent radiation source.
53. Apparatus for obtaining image data for an object as claimed in claim 50 or claim 53 wherein said radiation source comprises an incoherent radiation source.
54. Apparatus for obtaining image data for an object as claimed in any one of claims 50 to 53 wherein said object is located between said radiation source and said aperture.

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55. Apparatus for obtaining image data for an object as claimed in any one of claims 50 to 54 wherein said aperture is located between said radiation source and said object to be imaged.
56. Apparatus for obtaining image data for an object as claimed in any one of claims 50 to 55 wherein said means to move said aperture comprises a micro-actuator.
57. Apparatus for obtaining image data for an object as claimed in any JO one of claims 50 to 56 wherein said means to process said intensity data comprises: a microprocessor; and a data carrier comprising instructions for said microprocessor to perform an analysis of said data; and a data input device configured to allow a user to input instructions; and means to instruct a movement of said aperture via said aperture movement means.
58. Apparatus for obtaining image data for an object as claimed in any one of claims 50 to 57 further comprising at least one lens located between said aperture and said detector, said lens configured to alter a camera length of said apparatus.
59. Apparatus for obtaining image data for an object as claimed in any one of claims 50 to 58 further comprising at least one lens located between said 3 0 object and said radiation source.

P1 059.spec
60. Apparatus for constructing image data for a region of an object comprising: means to analyze an intensity data of a diffraction pattern arising from said region, said intensity data arising from a function of a known aperture, wherein said aperture can be moved to at least two different positions relative to said object.
61. Apparatus for obtaining image data for an object comprising: (i) means to obtain a first diffraction pattern of said object where an aperture is in a first position; and (ii) means to obtain a second diffraction pattern of said object where said aperture is in a second position; and (iii) means to measure an intensity of said first diffraction pattern; and (iv) means to measure an intensity of said second diffraction pattern; 2 0 and (v) means to approximate a phase of said first diffraction pattern; and (vi) means to combine said phase and said measured intensity of said 2 5 first diffraction pattern to form a wave function of said first diffraction pattern; and (vii) means to transform said wave function of said first diffraction pattern to obtain an estimate of a wave function of said object where said aperture is in a first position; and P1059.spec (viii) means to transform said estimate of said wave function for said object where said aperture is in said first position to an estimate of a wave function for said object where said aperture is in said second position; and (ix) means to transform said wave function of said object where said aperture is in said second position to obtain an estimate of said wave function of said diffraction pattern where said aperture is in said second position; and (xi) means to modify said wave function of said diffraction pattern when To said aperture is in said second position using said measured intensity of said second diffraction pattern; and
62. Apparatus for obtaining image data for an object comprising: (a) means to obtain a plurality of diffraction patterns from a plurality of aperture positions, each said diffraction pattern corresponding to a known aperture position of said plurality of aperture positions, and; (b) means to measure an intensity pattern of each said diffraction To pattern; and (c) means to approximate an exit wave function of said object; and (d) means to transform said approximation of said exit wave function of z5 said object using a known aperture transmission function for each said aperture position to obtain a corresponding overall exit wave function for each said aperture position; and (e) means to transform each said overall exit wave function, to obtain a o corresponding wave function in diffraction space; and P1 059.spec (f) means to modify each said wave function in diffraction space using said measured intensity patterns at each said aperture position, whilst preserving a phase of each said wave function in diffraction space to obtain a corresponding respective refined wave function in diffraction space for each said aperture position; and (g) means to transform each said refined wave function in diffraction space to obtain a corresponding respective refined overall exit wave function for at each aperture position; and (h) means to obtain a corresponding respective value of said exit wave function for each said aperture position; and (i) means to obtain an average value of said exit wave function from s said plurality of values of said exit wave function; and (j) means to repeat (d) to (h) to obtain a refined exit wave function of said object.

P1059.spec