Patent Application
20130120813
The present invention relates to improvements in or relating to holography, and in particular to methods for generating holograms, together with associated apparatus for carrying out those methods. The improvements of this disclosure are applicable to holography for any purpose, for example, but without limitation, to the sphere of manufacturing processes such as photolithography, or to the sphere of consumer electronics products, such as holographic television or other devices.
As an example only, we discuss the field of lithography. Standard lithographic procedures, such as proximity and projection exposure, do not work well for non-planar substrates. Any conventional imaging system is limited by the depth of its point spread function. The image will become blurred or distorted away from its focal plane, leading to variation in feature width or to insufficient energy density for a well defined photoresist exposure.
Instead of a standard photomask, computer generated holograms (CGH) have been used to create focused patterns on 3D substrates [1, 2]. This method has hitherto been limited to the imaging of simple sparse line patterns. For more complex or dense patterns, mask implementation can become a problem as simultaneous modulation of amplitude and phase may be required.
It is known to employ wave-optics for enhanced photo-lithography. Simple serifs in lithography are applied to dampen the effects of diffraction. Also, fully diffraction simulated or analytical solutions have been investigated for planar and non-planar systems [11, 5, 2]. In planar systems, little advantage over existing proximity/contact techniques have been found but for non-planar substrates, diffractive masks have an advantage over simple proximity masks because patterns imaged over such substrates imaged by conventional means are severely degraded by diffraction effects. In contrast, properly implemented diffractive masks are capable of focusing patterns over a variable depth surface with relative ease.
There are existing methods for designing diffractive masks for photolithography over non-planar substrates: in the field of photolithography, superimposed holographic analytical line solutions have been utilised as a useful exposure technique for grossly non-planar substrates down to 5 -10 μm feature size[1] or over a depth of up to several cm [14] (see also [12]).
Such solutions however are not without problems. The simple numerical propagation and analytical solutions used to generate useable CGH patterns often require both phase and amplitude modulation which can be difficult and time consuming to fabricate; quantised amplitude-only reconstructions exhibit limited diffraction efficiency and tend to lead to low image fidelity and phase-only analytical approaches suffer from serious limitations in the geometry and density of line patterns
Iterative techniques are more suitable for maximising diffraction efficiency and have been used to generate diffractive optical masks for arbitrary intensity patterns over planar substrates. Iterative optimisation procedures based on the Gerchberg-Saxton (GS) algorithm [3] allow for a more general pattern geometry to be generated whilst maintaining a phase only CGH. However, holograms generated in this way will tend to produce large noise components in the reconstructed image, resulting in poor photoresist exposures. Others have overcome this by time averaging using an active modulation device [4] or have applied more complex systems and modeling techniques [5]. However, these methods are applied to planar substrates only. Accordingly, there is still a need for improvement with respect to 3D holography.
According to a first aspect of the present disclosure, there is provided a method of generating a wave-optical exposure mask comprising:
The multiple planes may be planes which are cross-sectional (x,y) with respect to, and provided at different positions along, an optical axis, z, extending from the diffraction plane.
Optionally, said iterative process includes:
Optionally, the iterative process further includes filtering and spatial constraints applied at the diffraction plane.
Optionally, amplitude correction is applied to only a sub-portion of each image plane where the sampled pixels intersect a pseudo-continuous surface function.
Optionally, amplitude and phase information is unconstrained in unimportant selected areas of an image volume such as to allow the convergence of the algorithm. The amplitude and phase information may also be discarded where it is known that the surface prevents propagation.
Optionally, a propagation routine adopted to move between image planes and hologram is that of a convolution form of the Fresnel diffraction integral.
Alternatively, said propagation routine is an application of a Rayleigh-Somerfield propagator.
Alternatively, said propagation routine is an angular spectrum method.
Optionally, each image plane is corrected with an ideal amplitude profile, whilst retaining the propagated phase.
Optionally, the hologram plane itself is corrected with unit amplitude to give a phase only pattern.
According to a second aspect of the present disclosure, there is provided a wave-optical method of generating a hologram comprising:
Steps forming optional parts of the first aspect as described above may be applied also to the method of the second aspect.
According to a third aspect of the present disclosure, there is provided an apparatus for generating a hologram having a desired non-planar pattern in object space, comprising:
Optionally, said modulator comprises a spatial light modulator (SLM).
Optionally, said radiation source comprises a laser.
According to a fourth aspect of the invention, there is provided a lithographic apparatus comprising the apparatus of the third aspect and arranged for carrying out the method of the first and/or the second aspect.
According to a fifth aspect of the invention, there is provided a consumer device for generating holograms which includes the apparatus of the third aspect and/or is arranged for carrying out the method of the first and/or second aspects.
Optionally, said consumer device comprises a holographic television with suitable projection means for projecting a hologram according to said predefined pattern into a viewing space or a display to be viewed by a user.
According to a sixth aspect of the present invention, there is provided a computer program product including instructions that, when run on an computer, enables said computer to implement the method of the first or second aspects, or to form part of the apparatus of the third, fourth or fifth aspects.
The present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:
The present disclosure relates to a method of generating a wave-optical exposure mask that confines an incident coherent or partially-coherent wave according to a specified non-planar intensity pattern. A partial, multi-plane reinforcement method is disclosed that enables convergence to a suitable exposure mask with minimal error. The method consists of an optical design means that is subject to two fundamental constraints: Firstly, the specified intensity pattern is defined over a bounded three dimensional geometrical surface of the mathematical form z=f (x,y) by a series of multiple cross-sectional planes. Secondly, the exposure mask is intentionally confined to a defined discrete array of amplitude and/or phase altering elements to yield a diffractive optical mask.
The Gerchberg-Saxton [3] iterative phase reconstruction algorithm comprises a simple sequence which, when repeated, can converge to a hologram phase pattern given a pair of intensity conditions for hologram and image planes. Many variations and derivations of this algorithm have been applied to optics problems and, importantly, for both paraxial optical and far-field problems for which rapid algorithms such as the Fast Fourier transform (FFT) and the convolution form of the Fresnel diffraction equation may be implemented.
Generalisation of this approach beyond single image planes into a multiple output image planes which are propagated between in each iteration leads to methods for wave-optical mask design constrained to patterns on three dimensional planes. This in turn generates a quantised diffractive optical element which produces images at multiple depths.
In this method, restrictions are imposed across the entirety of every image plane in succession, by means of optical propagation between each neighbouring image plane. This computationally heavy approach has been successfully applied when the spacing between the multiple image planes is large in comparison to the general offset distance (defined as the distance between the diffractive element and the iteration plane nearest to the diffraction element (distance Z2 in
The inventors have found that an iterative algorithm based on the Fresnel or angular-spectrum transformation can converge to holograms of continuous patterns for “thin” (on the order of the width of the point spread function) binary images. These are suitable for patterning of integrated circuit interconnections in a lithographic exposure. These methods are usually applied to a single planar image. To extend this method to 3D surfaces we have investigated multi-plane algorithms that are similar to those discussed in [6-8, 13] for display and optical tweezers applications, and have extended the constraints such that it becomes possible to form a continuous exposure pattern.
Rather than a single output plane image, the algorithm invokes a numerically evaluated angular-spectrum propagation [9] between uniformly spaced planes inside an image volume and a single input diffraction plane. The process may be outlined as:
In step (IV), altering and spatial constraints may also be applied. As with the GS algorithm, the above process is repeated, and we expect the error to reduce in both the hologram and image.
Breaking the longer propagation transforms (I,III) into multiple steps allows the image to be calculated without incurring noise which would be caused by aliasing of the transfer function [10].
Separate amplitude constraints are applied on each image plane as shown by our test geometry in
To enable the algorithm to converge to a useful solution the image volume must not be over-constrained. A simple approach is therefore to constrain only those areas on each plane that intersect with the target surface. We also ensure that the pattern contains no constrained area that is directly occluded by another along the optical axis. This was shown to be able to produce relatively sparse image zones in [7], however we constrain ourselves to a real surface and endeavor to show experimentally that a continuous pattern can be generated onto photoresist, i.e. under constraints that are much tighter than those required for display applications. Within the constraint process, “high” regions are given field amplitude value 1 and low regions are set to 0.1 whilst phase is unchanged. Unconstrained areas remain unchanged in phase or amplitude. As discussed in [8], low regions cannot be set to zero as this would lead to a loss of phase information between propagation steps. The high/low ratio was chosen such as to enforce as large a contrast as possible without over-constraining the requirements on the image field.
The choice of “seeding” hologram to initialize the algorithm will influence the structure of the resulting pattern. A random phase distribution is often used but we have observed more reliable quality and faster convergence when applying an analytically derived initial hologram. Line segment holograms [2] can be used to generate image lines. To generate the initial hologram, we superimpose planar line segment holograms and then confine the resulting pattern to a phase-only distribution. This produces a non-ideal starting hologram, which is refined by the iterative procedure. Mathematically this approximation takes the form
where d=(y−pm−s) and y is the y direction coordinate of the hologram, p is the pitch of the lines to be imaged, s is an offset for alignment, M is the number of lines, and U is the hologram pattern. λ is the nominal wavelength of the illumination source. The 2D “rect” function limits the size of the hologram according to A and B where these are determined by the length of the lines and the width of the hologram respectively. A final further step is performed to curtail this to a phase only pattern.
When the plane separation is not large in comparison to the general offset distance it becomes difficult to constrain the problem because of the restriction that every pixel is constrained according to the desired image for every image plane. This becomes overly strict when it is considered that the image pattern need only be reinforced at the locations at which certain pixels intersect the surface function z=f (x,y). For most practical situations this leads to a greatly reduced degree of overall constraint to be applied in each image plane.
Taking the standard Gerchberg-Saxton routine, modification to add multiple planes [7,8] requires that, before propagating to the hologram plane, multiple planes in the image volume are successively calculated by short propagations between each plane, starting with the furthest, again as shown in
For non-planar photo-lithography and other high fidelity 3D patterns this method becomes inadequate when planes with different values enforced in the same x-y coordinate area are pushed close together. This conflicting reinforcement stifles the ability of the algorithm to achieve sufficient contrast between a high intensity pixel in one image plane and low intensity pixel in the corresponding pixel of a neighbouring image plane. This presents an impractical constraint on the diffractive mask for larger patterns imaged over pseudo-continuous three dimensional surfaces.
The method of partial reinforcement proceeds by amplitude correction of only a sub-section of each image plane where the sampled pixels intersect the pseudo-continuous surface function, as shown in
As an example, a propagation routine adopted to move between image planes and the hologram is that of a convolution form of the Fresnel diffraction integral [9,10].
And |U(ξ, η) is the hologram plane field, V(x,y) is output plane field, z is distance along the optical axis, λ is wavelength and k=2π/λ. This convolution, evaluated numerically by applying a forward and inverse fast Fourier transform, leads to a relatively efficient calculation which retains 1:1 sample spacing on all input and output planes.
This propagation routine implemented numerically is immediately appropriate because of the retention of sample spacings and the validity of the propagation under short distances. Other routines however are just as viable, the angular spectrum method which retains the same advantages but has potential to propagate through rotation, this would mean that certain piecewise planar surfaces can be calculated with much greater efficiency. Another approach is application of Rayleigh-Somerfield propagator which at the expense of computation time increases the flexibility of the approach even further.
With any convolution based transformation (Fresnel, Angular-Spectrum and
some arrangements of Rayleigh-Sommerfeld), when evaluated numerically, the
transfer function (TF) may be calculated in the frequency domain. This avoids
un-necessary FFT operations. Expressed mathematically with the angular spectrum TF considered we have:
V(x,y)=−1(
(U(ξ,η)×H(vx, vy))
where
H(vx,vy)=ej2πz√{square root over ((1/λ)2+vx23+vy2)}
Where F is the Fourier transform (which would be evaluated using an FFT) and vx and vy are coordinates in the spatial frequency domain.
Adding still further to the completeness of the model, another constraint can be applied to planes within sections where our surface to be imaged upon is occluded by its geometry. As such we discard all amplitude and phase information where we know that the surface prevents propagation thus moving away from a completely free volume propagations into one that takes into account obstacles and occlusions.
Some implementations would constrain the iteration propagations to the sample spacings of the implementation medium, i.e. pixel pitch on the Liquid Crystal On Silicon (LcoS) Spatial Light Modulator or phase-only optic. This is improved by a routine which samples at above the implemented device pitch and imposes an sampling constraint at the hologram plane.
Combining these modifications to this multiple-plane iteration together with a set of depth masks and an array of closely spaced planes to propagate between therefore allows the algorithm to converge for different types of three dimensional surface geometries.
We turn now to discuss some examples of how these techniques can be applied. These examples are not limiting to the scope of the invention.
Running simulations with a sample pitch of 4 μm in both x & y and an image size of 8.192 mm×8.192 mm, we produce an image of a bus comprising 8 lines which descend a 45° slope and a total depth of z2=4.096 mm, as shown in
A set of holograms was generated, each by 50 iterations, using varying N (and subsequently δz). Example image line profiles and cross sections can be seen in
Images generated were assessed according to the contrast parameter C=(H−L)/(H+L) [11] shown in
Fluctuations present in the graph demonstrate high sensitivity to the local defects which may be generated by the iterative process. If we choose for our minimum quality C to be above 0.6 as quoted as an approximate limit for lithography in [11] then this strict “worst-case” metric shows that for our simulations at δz˜228 μm and below, a consistent and usable image may be generated. This value equates to δz˜0.25×DOF for this system at z˜16.2 mm. This procedure can therefore result in a well defied continuous image which we have verified experimentally. A set of test exposures were performed to show our continuous pattern in the focal region. The hologram generated using N=19 (δz=228 μm) was used as this is close to the lowest computing effort for a viable result. The optical setup is shown in
The hologram was implemented on an 8 μm sample pitch phase-only spatial light modulator (SLM “Pluto” from Holoeye Photonics AG) by re-sampling the simulated hologram. This device is illuminated by an on-axis expanded laser beam (Coherent “Cube” 405 nm 50 mW). The photoresist used was “BPRS200”. This layer was approximately 2 μm thick.
Two images of the pattern developed on a coated substrate are shown in
Continuous lines of requisite shape can be seen on both at and tilted sections with only small line width variation noticeable at the edges of constraint areas on separate planes.
In conclusion we have shown that simple phase only holograms generated by an iterative method can be used to produce continuous patterns of dense lines suitable for microelectronics fabrication on grossly non-planar substrates. We have presented an example where 8 lines of pitch 24 μm have been patterned onto a slope which is more than four times deeper than the depth of focus of the optical system. This is beyond the capabilities of a conventional optical projection system with a similar resolution limit.
In one or more exemplary embodiments, the functions and configurations described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a computer. By way of example such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. The instructions or code associated with a computer-readable medium of the computer program product may be executed by a computer, e.g., by one or more processors, such as one or more digital signal processors (DSPs), general purpose microprocessors, ASICs, FPGAs, or other equivalent integrated or discrete logic circuitry.
Various improvements and modifications can be made to the above without departing from the scope of the invention.
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| Number | Date | Country | Kind |
|---|---|---|---|
| 1004247.1 | Mar 2010 | GB | national |
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/GB2011/050509 | 3/15/2011 | WO | 00 | 10/15/2012 |
