Light field imaging based on tilt aberration

Abstract

A method of obtaining a transverse phase gradient of a wave field from at least a first and a second wave field intensity map is disclosed, comprising the steps of: capturing the first wave field intensity map of a target at a first incoherent gradient aberration degree with a first incoherent gradient aberration using a filter positioned between an electromagnetic radiation source and an electromagnetic radiation detector that captures the first wave field intensity map; capturing the second wave field intensity map of the target at a second incoherent gradient aberration degree with a second and different incoherent gradient aberration using a filter positioned between an electromagnetic radiation source and an electromagnetic radiation detector that captures the second wave field intensity map; determining the transverse phase gradient based on at least a difference in logarithms of the wave field intensity maps divided by a magnitude of the difference between the first incoherent gradient aberration and the second incoherent gradient aberration. Use of the imaging system, computer program product and method are further disclosed.

Description

[Technical field]

[0001] The present invention relates to a method for acquiring the transverse phase gradient of a wave field The present invention further relates to the use of an imaging system, a computer program product and the method for performing the method. [Background technology]

[0002] Quantitative reconstruction of the complex optical wave field allows prediction of its temporal evolution and energy flow. This capability is revolutionary for imaging, enabling new experimental realizations (e.g. lensless imaging), the exploitation of phase as contrast due to properties of the medium of interest (e.g. thickness, refractive index, electromagnetic field, crystallography, etc.), and characterization and correction of aberrations (e.g. for adaptive optics, light field imaging, digital refocusing, etc.).

[0003] Examples of such methods include differential interference contrast, classical ptychography, Fourier ptychography, TIE / defocused imaging, holography, microlens arrays, Shack-Hartmann sensors, grating phase contrast, and speckle tracking.

[0004] These methods have led to major advances in biological, geological and materials research, which in turn has created a continuing need for new methods that are faster, more accurate and more robust. Summary of the Invention [Problem to be solved by the invention]

[0005] In particular, there is a need for a method of obtaining the phase gradient of a light field that is versatile and stable, as well as simple, fast and inexpensive to implement. [Means for solving the problem]

[0006] One aspect of the invention relates to a method of obtaining a transverse phase gradient of a wave field from at least a first wave field intensity map and a second wave field intensity map, the method comprising: - capturing a first wave field intensity map of a target with a first incoherent gradient aberration using a first filter having an attenuation profile with continuous derivatives, the first filter being positioned between an electromagnetic radiation source and an electromagnetic radiation detector that captures the first wave field intensity map; - capturing a second wave field intensity map of the target with a second incoherent gradient aberration using a second filter having an attenuation profile with continuous derivatives, the second filter being positioned between an electromagnetic radiation source and an electromagnetic radiation detector that captures the second wave field intensity map, the second incoherent gradient aberration being different from the first incoherent gradient aberration; - determining the transverse phase gradient based on a difference in logarithms of wave field intensity maps divided by a magnitude of a difference between at least the first incoherent gradient aberration and the second incoherent gradient aberration. Includes.

[0007] Electromagnetic radiation, such as light, is associated with a complex wave field Ψ, which has real (amplitude) and imaginary (phase) components, and is represented by the form Ψ(x,y)=A(x,y)e iφ(x,y) where A is the amplitude, φ is the phase, and x and y are spatial coordinates in the relevant plane that is transverse to the direction z of propagation of the wave field. The z-axis may also be referred to as the optical axis. The optical axis defines a line along which there is a degree of rotational symmetry in an optical system, such as an optical imaging system, including a camera system or a microscope system. The optical axis is an imaginary line that defines a path along which radiation propagates through the system to a first approximation.

[0008] Throughout this disclosure, electromagnetic radiation may be referred to as light, however, it should be understood that descriptions relating to light may equally apply to other forms of electromagnetic radiation other than light.

[0009] The phase of light contains valuable information about light, such as information about the propagation of the light. One example is that the phase can be used to determine the direction of light propagation. This is true because measuring the direction of light is the same as measuring the gradient of the optical phase. θ x =dφ / dx θ y =dφ / dy Here, θ x and θ y represents the angles in the directions x and y perpendicular to the optical axis (z-axis).

[0010] The problem with measuring light intensity is that I(x,y)=|Ψ(x,y)| 2 =A(x,y) 2 As is evident from, phase information is lost in the intensity; this problem of loss of information about phase that typically occurs when this physical measurement is performed is commonly referred to as the "phase problem".

[0011] The method of the present invention provides an advantageous way of obtaining phase information from light intensity, solving the phase problem mentioned above. This provides a new and advantageous route to light field imaging. As an example, the method of the present invention is particularly suitable for microscopic studies of cells and other biological objects that tend to be nearly transparent and therefore difficult to image using conventional microscopes. The use of the method may enable the acquisition of structural information about biological objects that cannot be obtained using conventional optical microscopy techniques. The method of the present invention achieves this in a rather counterintuitive way by specifically exploiting a particular class of imperfections that are commonly present in imaging systems.

[0012] All physical imaging systems are inherently aberrated, meaning that the (usually two-dimensional) intensity of the output field differs from that of the field input to the imaging system. Optical aberrations can be classified into two types of aberrations: coherent and incoherent aberrations. Coherent aberrations only affect the phase of the wave field and are therefore complex, i.e. e if(x,y) Examples of coherent aberrations include defocusing and spherical aberration. Incoherent aberrations, of which Gaussian blur and the Airy disk are examples, only affect the amplitude of the wave field and are therefore real, i.e., e f(x,y) A particularly common aberration is the incoherent tilt aberration, where the aberration function f(x,y) is, for example, τ(x,y) It is noted that although it is referred to as incoherent tilt, this aberration does not require a physical tilt (change in angle) of any of the physical components of the optical system.

[0013] Optical aberrations are present in most imaging systems, so these aberrations are also present in microscopy systems. The intuitive routine of most microscopists would be to use an aberration balancing method to correct or a digital wavefront correction based on an iterative engine procedure to undo the tilt-induced aberrations. However, it is counter to the norm to exploit microscopy imaging contaminated by incoherent tilt aberrations to perform deterministic phase acquisition without imposing any assumptions on the imaged target / object. Nevertheless, this is precisely what can be achieved by the method of the present invention.

[0014] The method according to the present invention is advantageous for several reasons.

[0015] First, the method can be used in a number of applications and devices, including computational imaging devices such as cell phone cameras (particularly for refocusing images) for rapid quantitative phase contrast imaging of cells and other biological objects, ptychographic microscopy, augmented reality systems (particularly for distance measurement) and virtual reality video capture systems (particularly depth of field).

[0016] Second, the method is analytical and therefore does not necessarily rely on numerical solutions, which makes the method simple and fast and therefore usable in and for many applications.

[0017] Third, the method does not require any a priori assumptions about the target of interest / being studied, which potentially provides a much faster and more robust method than existing methods of, for example, light field imaging.

[0018] Furthermore, the method is advantageous for the same reasons that other light field imaging systems and methods are advantageous: for example, in accordance with the present invention, it may be possible to refocus an image after it has been obtained.

[0019] In the context of the present invention, a "wave field" can be understood as the space in which electromagnetic waves propagate, including at least microwaves, infrared light, visible light, ultraviolet light and X-rays.

[0020] In the context of the present invention, a "wave field intensity map" can be understood as a two-dimensional mapping of electromagnetic radiation intensity in an image plane intersecting the direction of propagation of the wave field. In other words, the wave field intensity map can be considered as an image depicting radiation intensity. For example, if the electromagnetic radiation is light, the wave field intensity map can be an image depicting light intensity.

[0021] In the context of the present invention, a "target" should be understood as any kind of physical object / subject that can be exposed to incident electromagnetic radiation and that can scatter the electromagnetic radiation. For example, if the electromagnetic radiation includes light, the target may be an object / subject that must be studied using light. The light incident on the target can be scattered from the target and recorded to provide an image of the target.

[0022] In the context of the present invention, "incoherent tilt aberration" should be understood as any kind of deviation in the wave field induced by geometric changes to the components of the imaging system, such as, for example, the displacement of the electromagnetic radiation source, the displacement of the target, and the displacement of the filters. It should be readily understood that the tilt does not necessarily require a physical tilt (i.e., a change in angle) of the physical components of the optical system, since the effect of the incoherent tilt aberration can equally be obtained through other geometric changes than the tilt of the components.

[0023] More specifically, the slope is:

number

number

number

number

number

number

[0024] In the context of the present invention, a transverse phase gradient is to be understood as a phase gradient that is transverse to the optical axis of the imaging system.

[0025] In the context of the present invention, a "filter having an attenuation profile with continuous derivative" is understood as a filter configured to attenuate electromagnetic radiation, the attenuation being described by a profile in which the derivative of the attenuation profile with respect to position is continuous within the working area of ​​the filter. The continuous derivative may be a variable continuous derivative or a constant continuous derivative. The use of such a filter may be:

number

number

[0026] In the context of the present invention, an "electromagnetic radiation source" is to be understood as any type of radiation source capable of providing electromagnetic radiation. For example, the radiation source may be a light source, such as a light emitting diode (LED), if the electromagnetic radiation comprises visible light.

[0027] The electromagnetic radiation source may include one or more individual electromagnetic radiation sources. For example, it may be a single radiation source or it may be multiple radiation sources distributed in any configuration. The electromagnetic radiation source may include a first electromagnetic radiation source and a second electromagnetic radiation source, the two radiation sources being two separate entities. As an example, the electromagnetic radiation source may be a light source implemented as LEDs on a light guide plate. This allows the angle of incidence of the light on the target to be changed by switching between lighting the individual LEDs.

[0028] In the context of the present invention, an "electromagnetic radiation detector" is to be understood as any kind of device capable of recording / capturing a wave field intensity map. For example, the electromagnetic radiation detector can be a camera.

[0029] In one embodiment of the invention, the first wave field intensity map and the second wave field intensity map represent intensity of light, the light including frequencies in the range of 400 nanometers to 700 nanometers.

[0030] In alternative embodiments of the invention, the first and second wave field intensity maps may represent the intensity of microwave radiation, infrared radiation, ultraviolet radiation or x-ray radiation.

[0031] In the context of the present invention, the "difference of the logarithms of the wave field intensity maps" should be understood as the difference between the logarithm of the intensity (intensity value) of the first wave field intensity map and the logarithm of the intensity (intensity value) of the second wave field intensity map. According to an embodiment of the present invention, these intensities may correspond to exactly the same pixels, i.e. pixel positions, in the two wave field intensity maps. The skilled person will easily understand that the difference of the logarithms may also mean the logarithm of a fraction, i.e. loga-logb=loga / b. It should also be noted that according to the method of the present invention, the use of logarithms may mean the use of an approximation of the logarithm. For example, the logarithm may be approximated, for example, using a Taylor expansion. The use of an approximation of the logarithm and thus of the difference in the logarithms may be specific to certain implementations of the method, such as computer implementations, where the computational expense of performing element-wise logarithms on large wave field intensity maps may be significantly reduced by the use of such an approximation.

[0032] According to the present invention, it is envisaged that the electromagnetic radiation sources used in the steps of capturing the first and second wave field intensity maps may be the same electromagnetic radiation source or different electromagnetic radiation sources. For example, a first electromagnetic radiation source may be used in capturing the first wave field intensity map, and a second electromagnetic radiation source different from the first electromagnetic radiation source may be used in capturing the second wave field intensity map. If the electromagnetic radiation sources are the same, it should be understood that they are the same physical entity. In a similar manner, a first filter is used in capturing the first wave field intensity map, and a second filter is used in capturing the second wave field intensity map. The first and second filters may be the same filter, i.e. they are the same physical entity, or they may be different filters. Similarly, an electromagnetic radiation detector is used in capturing the first wave field intensity map, which may be referred to as a first electromagnetic radiation detector, and an electromagnetic radiation detector is used in capturing the second wave field intensity map, which may be referred to as a second electromagnetic radiation detector. The first and second electromagnetic radiation detectors may be the same electromagnetic radiation detector, i.e., they are the same physical entity, or they may be different electromagnetic radiation detectors. It is contemplated that any combination of electromagnetic radiation sources, filters and electromagnetic radiation detectors may be used in accordance with the methods of the present invention.

[0033] As a first example, a single electromagnetic radiation source may be used with a first filter, a second filter (the two filters being two separate filters) and a single electromagnetic radiation detector (a single entity). As a second example, a single electromagnetic radiation source may be used with a single filter (i.e. one physical entity that is a filter) and a single electromagnetic radiation detector (a single entity). As a third example, a first electromagnetic radiation source and a second electromagnetic radiation source (the two radiation sources are two separate radiation sources) may be used with a first filter and a second filter (the two filters are two separate filters) and a single electromagnetic radiation detector (a single entity). As a fourth example, a first electromagnetic radiation source and a second electromagnetic radiation source (the two radiation sources are two separate radiation sources) may be used with a single filter (a single entity) and a single electromagnetic radiation detector. The above four examples may be further modified with an electromagnetic radiation source and a filter along with a first electromagnetic radiation detector and a second electromagnetic radiation detector (where the two detectors are two separate detectors), resulting in a total of eight examples of implementations of electromagnetic radiation sources, filters, and electromagnetic radiation detectors. Thus, one skilled in the art will readily appreciate that the presence (or absence) of designations such as "first" and "second" does not therefore dictate that any particular number of features must be used.

[0034] According to an embodiment of the invention, the difference between the first incoherent gradient aberration and the second incoherent gradient aberration is achieved by geometrically modifying one or more of the electromagnetic radiation source, the target and the first filter and / or the second filter.

[0035] In the context of the present invention, "geometrically modifying" includes modifying a position and / or orientation. Geometrically modifying one or more of the electromagnetic radiation source, the target and the first filter and / or the second filter should of course also be understood as the relative position and / or orientation between any of them may be modified.

[0036] Achieving differences in incoherent tilt aberrations by such geometrical modifications has the advantage that the amount of tilt can be determined precisely and therefore precisely taken into account in the method according to the invention.

[0037] According to an embodiment of the invention, the difference between the first tilt and the second tilt is realized by performing a geometric change of the electromagnetic radiation source. This geometric change may include a change in the position and / or orientation of the electromagnetic radiation source, thereby realizing a change in the illumination angle of the target. The change in position may be realized by a lateral displacement of the electromagnetic radiation source. For example, the electromagnetic radiation source may be physically moved in a plane perpendicular to the optical axis. In yet another embodiment of the invention, the illumination angle of the target is realized by switching from illuminating the target with a first electromagnetic radiation source to illuminating the target with a second electromagnetic radiation source.

[0038] According to an embodiment of the invention, the difference between the first and second tilt is realized by performing a geometrical change of the target. This geometrical change may comprise a change in position and / or orientation of the target. A change in position may for example be realized by a lateral displacement of the target.

[0039] According to an embodiment of the invention, the difference between the first and second tilts is realized by performing a geometric change of the filter having an attenuation with continuous derivative, which may include a change in the position of the filter, such as a change realized by a lateral displacement of the filter.

[0040] According to one embodiment of the invention, the geometrically modifying includes modifying one or more of an illumination angle of the target, a lateral displacement of the first filter and / or the second filter, and a lateral displacement of the target.

[0041] Achieving differences in incoherent tilt aberrations through such geometrical changes has the advantage that the amount of tilt can be determined precisely and accurately taken into account in the method according to the invention.

[0042] According to one embodiment of the invention, the geometric change comprises a change in the angle of illumination of the target by the electromagnetic radiation source. In other words, the electromagnetic radiation source can be displaced, such as displaced laterally, to illuminate the target with electromagnetic radiation from a different angle of incidence. Alternatively, mirrors can be used to steer illumination on the target.

[0043] According to one embodiment of the invention, the geometrical change comprises a lateral displacement of the first and / or the second filter.

[0044] According to one embodiment of the invention, the geometric change comprises a lateral displacement of the target.

[0045] Lateral displacement can be understood as the displacement that is transverse to the optical axis.

[0046] According to one embodiment of the invention, the electromagnetic radiation source used in capturing the first wave field intensity map is a first electromagnetic radiation source and the electromagnetic radiation source used in capturing the second wave field intensity map is a second electromagnetic radiation source, the second electromagnetic radiation source being displaced with respect to the first electromagnetic radiation source.

[0047] This provides an advantageous way of changing between a first incoherent gradient aberration and a second incoherent gradient aberration. By having two electromagnetic radiation sources that are displaced relative to each other, it is provided that the illumination angle of the target can be changed by switching from illumination from the first electromagnetic radiation source to illumination from the second electromagnetic radiation source.

[0048] For example, where the electromagnetic radiation includes light emitted from a light source, the two electromagnetic radiation / light sources may be individual LEDs.

[0049] According to an embodiment of the invention, the first filter and / or the second filter are Gaussian filters.

[0050] The Gaussian filter uses a Gaussian function, i.e., the shape f(x)=a·exp(-(xb) 2 / 2c 2 ) where a, b and c are constants and x is a variable, such as a variable related to position. Obviously, a Gaussian function has continuous derivatives, since the derivative of a Gaussian is itself a continuous function. Thus, an attenuation profile described by a Gaussian function is, by definition, also an attenuation profile with continuous derivatives. A Gaussian function has a first component, i.e., xb / c 2 also has a tilt aberration.

[0051] According to an embodiment of the invention, the first filter and / or the second filter are positioned between the target and the electromagnetic radiation detector.

[0052] According to an alternative embodiment of the invention, the first filter and / or the second filter are positioned between the electromagnetic radiation source and the target. It should be understood that when reference is made to "between", the filter is located between the target and the electromagnetic radiation detector along the optical axis.

[0053] According to an alternative embodiment of the invention, the first filter and / or the second filter are positioned between the electromagnetic radiation source and the target.

[0054] According to one embodiment of the invention, the first filter and the second filter are the same filter.

[0055] It should be understood that the same filter means that the first filter and the second filter are exactly the same physical entity, and not two separate filters of the same type. Note that the same physical entity may mean separate filters, or it may also mean a filter that is intrinsic to another optical component of the optical system, such as a lens.

[0056] According to one embodiment of the invention, the first filter and the second filter are different filters.

[0057] Different filters should be understood as meaning that the first filter and the second filter refer to two separate physical entities, but does not exclude that the two filters are dissimilar, in fact the filters may be identical in terms of type, optical properties and dimensions.

[0058] According to one embodiment of the present invention, the step of obtaining the phase gradient comprises the following steps:

number

[0059] The above-mentioned terms can be used when determining the transverse phase gradient. It should be noted that the terms only form part of the equation for determining the transverse phase gradient. In other words, there may be a correction factor applied to the terms, and thus the transverse phase gradient may only be proportional to the above-mentioned terms. However, this does not detract from the importance of the above-mentioned terms, which are in fact the main contribution according to the present invention.

[0060] As observed in the denominators of the above terms, the magnitude |τ 12 | is used. This quantity represents the magnitude of the difference in incoherent gradient aberration between two wave field intensity maps, i.e., the magnitude of the difference between the first incoherent gradient aberration and the second incoherent gradient aberration.

[0061] As observed in the numerator of the above term, the logarithmic difference of the wave field intensity maps is given by the following term: log(I 1 (x 1 ,y 1 ))-log(I 2 (x 1 ,y 1 ))

[0062] As can be seen in this section, the difference is the first intensity I 1 and the logarithmic expression containing the second intensity I 2 The first intensity is obtained by dividing the first intensity by the coordinate x 1 and y 1 and the second intensity is the intensity at the position referenced by coordinate x in the second wave field intensity map. 1 and y 1 is the intensity at the corresponding position, also referred to by

[0063] According to one embodiment of the present invention, the intensity I 1 and the intensity I 2 represent the intensities of corresponding pixels in the first wave field strength map and the second wave field strength map.

[0064] The method according to the invention involves determining the transverse phase gradient based at least on the difference of the logarithms of the wave field intensity maps. Specifically, this is the logarithm of the intensity values ​​of the respective wave field intensity maps used. In this embodiment of the invention, the first wave field intensity map and the second wave field intensity map are of similar dimensions, i.e., they can be described as having the same number and distribution of pixels, with each pixel being described as having a pixel intensity value or pixel intensity or intensity for short. For example, the wave field intensity maps may both include 512x512 pixels, 1024x1024 pixels, 1080x1920 pixels, 2048x2048 pixels or any other number and distribution of pixels. Regardless of the number and distribution of pixels, the wave field intensity maps are similar in this respect. Pixel I 1 and I 2 A transverse phase gradient is determined for each corresponding pair of , ...

[0065] According to one embodiment of the invention, the electromagnetic radiation detector comprises a camera.

[0066] The electromagnetic radiation detector may include a camera suitable for capturing the incident light and providing an image representation of the light.

[0067] According to one embodiment of the invention, the electromagnetic radiation detector used to capture the first wave field intensity map and the electromagnetic radiation detector used to capture the second wave field intensity map are the same electromagnetic radiation detector.

[0068] According to one embodiment of the invention, the method further comprises the step of generating a transverse phase gradient map and reproducing said transverse phase gradient map electronically, such as on an electronic display.

[0069] A lateral phase gradient map should be understood as an image depicting the lateral phase gradient.

[0070] According to an embodiment of the present invention, the step of determining the transverse phase gradient may include using a digital registration of the first wave field intensity map and the second wave field intensity map.

[0071] Digital registration should be understood as a computer-implemented process of transforming different sets of data into one coordinate system. Specifically, in the context of the present invention, the first and second wave field intensities may be different representations of the target due to the introduction of changes in incoherent gradient aberrations. Depending on the circumstances leading to the two wave field intensity maps, it may be necessary to perform digital registration to ensure that the wave field intensity maps can be properly compared, i.e. that it is the correct difference of the logarithms of the intensities produced. In fact, digital registration may involve shifting the wave field intensity maps relative to each other so that they are in alignment with respect to common features present in both wave field intensity maps. This means that the coordinates (x 1 ,y 1 ) corresponds to a common feature location on the target.

[0072] According to one embodiment of the invention, the attenuation profiles of the first and second filters have variable continuous derivatives.

[0073] In the context of the present invention, a "variable continuous derivative" of an attenuation profile should be understood by the way in which the derivative of the attenuation profile varies in space, not in time. The derivative of the attenuation profile referred to in the previous disclosure is the derivative of the attenuation of the filter with respect to position. In the present embodiment, this derivative is variable in space, meaning that it takes on different values ​​in space / position. An example of an attenuation profile exhibiting such behavior is a Gaussian type attenuation profile. The derivative of a Gaussian function with respect to its variable (in this case the variable is position) is also a Gaussian function, which is a continuous function that takes on different values ​​depending on the variable. The derivative of such an attenuation profile therefore exhibits a variable continuous behavior.

[0074] It should be noted that since the first and second filters may be different according to an embodiment of the present invention, the variable continuous derivative of the attenuation profile may not be the same variable continuous derivative for the first and second filters. Thus, this embodiment should be understood generally as the first and second filters having variable continuous derivatives, and the attenuation profiles (as well as the derivatives) of the first and second filters may be different.

[0075] According to another embodiment of the invention, the attenuation profiles of the first and second filters have constant continuous derivatives.

[0076] In the context of the present invention, a "constant continuous derivative" of the attenuation profile should be understood in the manner in which the derivative of the attenuation profile is constant in space, but not in time. The derivative of the attenuation profile referred to in the preceding disclosure is the derivative of the attenuation of the filter with respect to position. In the present embodiment, this derivative is constant in space, which means that the derivative takes the same value in space / position. An example of an attenuation profile exhibiting such behavior is a first-order type attenuation profile, since the derivative of a linear function is a constant.

[0077] It should be noted that the constant continuous derivative of the attenuation profile may not be the same constant continuous derivative for the first and second filters, since the first and second filters may be different filters according to an embodiment of the present invention. Thus, this embodiment should be understood generally as the first and second filters having constant continuous derivatives, and the attenuation profiles (as well as the derivatives) of the first and second filters may be different.

[0078] Another aspect of the present invention is a method for producing a a source of electromagnetic radiation; - an electromagnetic radiation detector; - one or more filters having an attenuation with continuous derivatives, positioned between the electromagnetic radiation source and the electromagnetic radiation detector; - a computer processor; - a memory containing computer-implemented instructions which, when executed by said computer processor, perform the steps of a method according to any of the preceding provisions; wherein the imaging system is configured to be adjustable between a first degree of tilt and a second degree of tilt.

[0079] This provides an imaging system having the same advantages as mentioned in connection with the method according to the invention. In particular, an imaging system is provided having at least the following advantages:

[0080] First, imaging systems are versatile and can be used in a number of applications and devices, including computational imaging devices such as those in high-speed quantitative phase contrast imaging of cells and other biological objects, ptychographic microscopy, cell phone cameras (particularly for image refocusing), augmented reality systems (particularly for distance measurement) and virtual reality video capture systems (particularly depth of field).

[0081] Second, the imaging system operates according to analytical methods and therefore does not rely on numerical solutions, making it simple, fast and usable for many applications.

[0082] Third, the imaging system does not require any a priori assumptions about the target of interest / study, which potentially provides an imaging system that is much faster and more stable than existing systems, e.g., for light field imaging.

[0083] In one embodiment of the invention, the imaging system may further include additional optical components, such as one or more optical lenses.

[0084] In one embodiment of the present invention, the imaging system is implemented within a microscope for performing microscopy, such as optical microscopy.

[0085] In one embodiment of the present invention, the imaging system is implemented within a handheld electronic device, such as a smart phone.

[0086] In one embodiment of the invention, the one or more filters have an attenuation profile with variable continuous derivatives.

[0087] In one embodiment of the invention, the one or more filters have an attenuation profile with constant continuous derivatives.

[0088] Another aspect of the invention relates to a computer program product including instructions which, when executed by a computer processor of an imaging system, cause the computer processor to perform the steps of a method according to any of the above definitions.

[0089] Thereby, a computer program product (eg a piece of computer software) is provided which, when executed by a computer processor, achieves the same advantages as the method according to the invention.

[0090] Another aspect of the invention relates to the use of a method according to any of the above provisions and an imaging system according to any of the above provisions for contrast enhancement and / or digital refocusing.

[0091] According to further embodiments of the invention, the method and imaging system according to the invention may be used for refocusing, contrast enhancement and / or 3D reconstruction.

[0092] Various embodiments of the present invention will now be described with reference to the following drawings: [Brief description of the drawings]

[0093] [Figure 1] 1 shows an overview of a method according to an embodiment of the present invention. [Diagram 2] 1 illustrates an optical system according to an embodiment of the present invention and the induction of incoherent tilt aberration therein. [Diagram 3] 1 illustrates an optical system and the induction of incoherent tilt aberrations therein according to another embodiment of the present invention. [Figure 4] 1 illustrates an optical system and the induction of incoherent tilt aberrations therein according to another embodiment of the present invention. [Diagram 5] 1 illustrates an optical system and the induction of incoherent tilt aberrations therein according to another embodiment of the present invention. [Figure 6] 1 illustrates an optical system and the induction of incoherent tilt aberrations therein according to another embodiment of the present invention. [Figure 7] 1 illustrates an imaging system according to one embodiment of the present invention. [Figure 8] 4 shows a lateral phase gradient map obtained according to the method of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0094] 1 shows an overview of a method according to an embodiment of the present invention. The method includes three steps S1 to S3.

[0095] A first step S1 includes capturing a first wave field intensity map 1 of a target 4 at a first incoherent gradient aberration using a filter 5 having an attenuation profile with continuous derivatives, positioned between an electromagnetic radiation source 6 and an electromagnetic radiation detector 7 which captures the first wave field intensity map 1.

[0096] A second step S2 includes capturing a second wave field intensity map 2 of the target 4 at a second incoherent gradient aberration using a filter 5 having an attenuation profile with continuous derivatives, positioned between an electromagnetic radiation source 6 and an electromagnetic radiation detector 7 which captures the second wave field intensity map 2.

[0097] A third step S3 involves using the captured first wave field intensity map 1 and the captured second wave field intensity map 2 to determine the transverse phase gradient. The two captured wave field intensity maps are compared point by point (or pixel by pixel), specifically the intensity at a corresponding point / pixel on the two wave field intensity maps is used to obtain the transverse phase gradient at that point / pixel. The transverse phase gradient is determined by taking the difference in logarithms of the intensities and dividing by the magnitude of the difference between the first and second incoherent gradient aberrations. A transverse phase gradient map 3 can then be obtained based on the two wave field intensity maps.

[0098] It should be noted that Fig. 1 only serves to conceptually illustrate the operations underlying the method according to an embodiment of the invention, and the presentation of features on the figure is merely illustrative of the functionality of the features and does not limit the scope of protection defined in the claims. For example, although shown as a light bulb, the electromagnetic radiation source 6 is not limited to light bulbs and other electromagnetic radiation sources may be envisaged in this respect. The target 4 is shown conceptually (as an abstraction of a target) and any kind of target may indeed be envisaged in this respect.

[0099] 2a-b show two examples of optical systems according to an embodiment of the invention that are suitable for carrying out methods according to embodiments of the invention.

[0100] In FIG. 2a, an electromagnetic radiation source 6 is shown which is a light source. However, in other embodiments of the invention, the electromagnetic radiation source 6 can be a source of electromagnetic radiation other than a light source. The light source 6 illuminates a target 4 which is the sample under investigation in this embodiment. An example of such a sample can be a biological sample which has a tendency to be nearly transparent, making imaging of them using a conventional microscope difficult. Light scattered from the target 4 is collected by an objective lens 8 and passes through a filter 5. The filter 5 is characterized by having an attenuation profile, the derivative of the attenuation profile with respect to position being continuous within the working area of ​​the filter. In this example, the filter 5 is a Gaussian filter, but in other embodiments of the invention, the filter can be described by any other attenuation profile characterized by having a continuous derivative with respect to position within the working area of ​​the filter. The light leaving the filter 5 is collected in a tube lens 9 and guided towards an electromagnetic radiation detector 7 which in this embodiment includes a CCD (charge coupled device) and can image the light incident on the detector. This allows the electromagnetic radiation detector 7 to capture a wave field intensity map.

[0101] To better illustrate the method according to the invention, an electromagnetic radiation detector 7 captures a first wave field intensity map 1 in a system set-up shown in FIG. 2a.

[0102] In Fig. 2b the same optical system as in Fig. 2a is shown, but the filter 5 is displaced laterally (in the xy plane defined by the arrow in Fig. 2b) with respect to the optical axis 10. In this particular example shown in Fig. 2b, the filter 5 is displaced laterally in the y direction with respect to the optical axis (z direction, see also Fig. 2b). The effect of the lateral displacement of the filter 5 is to induce a change in the incoherent gradient aberration from a first incoherent gradient aberration in the case shown in Fig. 2a to a second incoherent gradient aberration in the case shown in Fig. 2b. As a result, the electromagnetic radiation detector 7 can capture a second wave field intensity map 2 using the configuration of the filter 5 as shown in Fig. 2b.

[0103] This captures two different wave field intensity maps (1 and 2), each associated with a particular incoherent gradient aberration and thus a particular incoherent gradient aberration. By utilizing step S3 shown in Figure 1, the wave field intensity maps captured in the case shown in Figures 2a-b can be used to determine the transverse phase gradient.

[0104] It should be noted that although FIG. 2b shows a lateral displacement in the y direction, any lateral displacement in the lateral plane (xy) can be used to induce a change in the incoherent gradient aberration.

[0105] 3a-b show two examples of optical systems according to further embodiments of the invention that are suitable for carrying out methods according to embodiments of the invention.

[0106] In figure 3a an optical system similar to that shown in figure 2a is shown. An electromagnetic radiation detector 7 is capable of capturing a first wave field intensity map 1 in a similar manner.

[0107] In Fig. 3b the same optical system as in Fig. 3a is shown, but the target 4 is displaced laterally (in the xy plane defined by the arrow in Fig. 3b) with respect to the optical axis 10. In this particular example shown in Fig. 3b, the target 4 is displaced laterally in the y direction with respect to the optical axis (z direction, see also Fig. 3b). The effect of the lateral displacement in Fig. 4 is to induce a change in the incoherent gradient aberration from a first incoherent gradient aberration in the case shown in Fig. 3a to a second incoherent gradient aberration in the case shown in Fig. 3b. As a result, the electromagnetic radiation detector 7 can capture a second wave field intensity map 2 using the configuration of the target 4 as shown in Fig. 3b.

[0108] This captures two different wave field intensity maps (1 and 2), each associated with a particular incoherent gradient aberration and thus with a particular incoherent gradient aberration. By utilizing step S3 shown in Figure 1, the wave field intensity maps captured in the case shown in Figures 3a-b can be used to determine the transverse phase gradient. Step S3 can be implemented as a digital registration step.

[0109] Although Figures 3a-b show that a change in the incoherent gradient aberration can be induced by a lateral displacement of the target 4, it should be noted that a change in the incoherent gradient aberration can also be induced by a rotation of the target 4 in the xy plane, i.e., a rotation in a plane that is lateral and orthogonal to the optical axis (or z axis).

[0110] 4a-b show two examples of optical systems according to further embodiments of the invention that are suitable for carrying out methods according to embodiments of the invention.

[0111] In Figure 4 an optical system similar to that shown in Figures 2a and 3a is shown. An electromagnetic radiation detector 7 is capable of capturing a first wave field intensity map 1 in a similar manner.

[0112] In Fig. 4b the same optical system as in Fig. 4a is shown, but the electromagnetic radiation source 6 is displaced laterally (in the xy plane defined by the arrow in Fig. 4b) with respect to the optical axis 10. In this particular example shown in Fig. 4b, the electromagnetic radiation source 6 is displaced laterally in the y direction with respect to the optical axis (z direction, see also Fig. 4b). The effect of the lateral displacement of the electromagnetic radiation source 6 is to induce a change in the incoherent gradient aberration from a first incoherent gradient aberration in the case shown in Fig. 4a to a second incoherent gradient aberration in the case shown in Fig. 4b. As a result, the electromagnetic radiation detector 7 can capture a second wave field intensity map 2 using the configuration of the electromagnetic radiation source as shown in Fig. 4b.

[0113] This captures two different wave field intensity maps (1 and 2), each associated with a particular incoherent gradient aberration and thus a particular incoherent gradient aberration. By utilizing step S3 shown in Figure 1, the wave field intensity maps captured in the case shown in Figures 4a-b can be used to determine the transverse phase gradient.

[0114] 4a-b show that a change in the incoherent gradient aberration can be induced by a lateral displacement of the electromagnetic radiation source 6, but it should be noted that a change in the incoherent gradient aberration can also be induced by changing the angle of illumination of the target 4.

[0115] 5a-b show two examples of optical systems according to further embodiments of the invention that are suitable for carrying out methods according to embodiments of the invention.

[0116] In Fig. 5a, two electromagnetic radiation sources 6 are shown: a first electromagnetic radiation source 5 (top radiation source 6 in Fig. 5a) and a second electromagnetic radiation source 6 (bottom radiation source 6 in Fig. 5a). Furthermore, the figure also shows two filters 5: a first filter 5 (top filter in Fig. 5a) and a second filter 5 (bottom filter in Fig. 5a). Each of the first and second filters 5 is characterized by having an attenuation profile with a continuous derivative with respect to position, similar to the filters shown in Figs. 2a-4b. As can be observed in the figure, the first and second filters 5 are located between the target 4 and the first and second electromagnetic radiation sources 6, respectively. The remaining part of the setup shown in Fig. 5a, on the right hand side of the target 4, is similar to the setups shown in Figs. 2a, 3a and 4a.

[0117] The electromagnetic radiation detector 7, in the configuration shown in FIG. 5a, is capable of capturing a first wave field intensity map 1.

[0118] Figure 5b shows the same optical setup as Figure 5a, but here electromagnetic radiation is provided by a second electromagnetic radiation source 6 rather than the first, and the electromagnetic radiation illuminates the target 4 through a second filter 5. As a result, the electromagnetic radiation detector 7 is able to capture a second wave field intensity map 2 using the configuration shown in Figure 5b.

[0119] This captures two different wave field intensity maps (1 and 2), each associated with a particular incoherent gradient aberration and thus a particular incoherent gradient aberration. By utilizing step S3 shown in Figure 1, the wave field intensity maps captured in the case shown in Figures 5a-b can be used to determine the transverse phase gradient.

[0120] This embodiment clearly shows a possible route to modify the angle of electromagnetic radiation incident on the target 4, and thus the incoherent gradient aberration, i.e. by switching from a first to a second (and relatively displaced) electromagnetic radiation source 6. If the electromagnetic radiation is light, the radiation source 6 can be an individual light source of an LED board.

[0121] Figures 6a-b show two cases of optical systems according to further embodiments of the invention suitable for carrying out methods according to embodiments of the invention. The embodiments are similar to the embodiment shown in Figures 5a-b, but instead of two filters 5 arranged between the electromagnetic radiation source 6 and the target 4, a single filter 5 is arranged between the objective lens 8 and the tube lens 9. Due to the change between the illumination of the target 4 by the first electromagnetic radiation source 6 and the illumination of the target 4 by the second electromagnetic radiation source 6, different incoherent gradient aberrations can still be realized in the wave field intensity map.

[0122] 7 illustrates an imaging system 11 according to one embodiment of the present invention. In this embodiment of the present invention, the optical system of imaging system 11 is shown as an optical microscope, however, according to alternative embodiments of the present invention, imaging system 11 may take other forms, such as a handheld electronic device such as a smartphone.

[0123] As can be seen in the figure, there is one electromagnetic radiation source 6, in this embodiment in the form of an LED, which is positioned to illuminate from below a target 4 received in an optical microscope. The target 4 may comprise a biological sample, such as, for example, cells, that may be difficult to observe using conventional optical microscopy. Above the target 4 are the optics of the microscope, including an objective lens 8, a tube lens 9 and a filter 5. The filter 5 is characterized by having an attenuation profile with a continuous derivative with respect to position. The filter 5 is configured to be translated in a plane perpendicular to the optical axis 10 (indicated by the x and y directions in the figure) to facilitate a change in the incoherent tilt aberration. The filter 5, which may be a Gaussian filter, is positioned in the infinity plane, i.e., between the objective lens 8 and the tube lens 9. As can be seen, the optical components of the objective lens 8, the tube lens 9 and the filter 5 are arranged along a common optical axis 10. At the top of the optical microscope there is an electromagnetic radiation detector 7, which is configured to detect light scattered by the target 4 and collected through the optics of the optical microscope.

[0124] By comparing Figure 7 with Figure 6, it becomes clear that the embodiment of Figure 7 can be regarded as a particular implementation of the embodiment of Figure 2 and thus the imaging system 11 of Figure 7 is also capable of performing steps S1 to S3 of the method described in relation to Figure 1.

[0125] The electromagnetic radiation detector 7 is communicatively associated with a computer processing arrangement 12, such as a personal computer. The computer processing arrangement 12 includes a memory 14 that may store a computer program product comprising computer readable instructions that, when executed by a computer processor 13 of the computer processing arrangement 12, cause the imaging system 11 to perform steps S1 to S3 of the method described in relation to Figure 1. The computer program product is loaded into the memory 14, although according to an alternative embodiment of the invention the computer program product may already be pre-stored on the memory 14, which is insertable into the computer processing arrangement 12.

[0126] The computer processing arrangement 12 is further communicatively associated with a screen 15 for displaying a transverse phase gradient map 3, e.g., a phase image. In this embodiment, the display 15 is shown as a desktop screen, however, this is merely illustrative of a possible type of display 15, and other types of displays are indeed envisaged according to other embodiments of the invention. For example, the display 15 can be the display of a smartphone (not shown).

[0127] Although computer processor 13 is shown together with an optical microscope and a display (in the form of a desktop screen), this is not intended to illustrate the only possible configurations of imaging system 11, and other implementations of imaging system 11 are indeed envisaged in accordance with other embodiments of the present invention. For example, imaging system 11 could form part of a smartphone (not shown).

[0128] FIG. 8 shows actual results obtained by the method according to the invention using a microscope. Two wave field intensity maps are captured: a first wave field intensity map 1 and a second wave field intensity map 2. The wave field intensity maps are with intensities from 0 to 4096, respectively. A scale bar with a length of 40 micrometers is shown adjacent to the wave field intensity maps. Each of the wave field intensity maps or images depicts the same cluster of human red blood cells at a magnification of 20×. The first and second wave field maps are obtained with opposite incoherent tilt aberrations corresponding to a + / −1.5 mm shift of a Gaussian filter placed in the infinity plane of the microscope, i.e. between the objective lens and the relay / tube lens 9 (not shown).

[0129] FIG. 8 also shows a transverse phase gradient map 3 obtained based on the first wave field intensity map 1 and the second wave field intensity map 2 using the method according to the invention. Along the transverse phase gradient map 3 (or transverse phase gradient image) a scale bar is shown indicating the value of the transverse phase gradient in radians / micrometer ranging from -π / 4 to π / 4. The transverse phase gradient map shows a clear phase gradient contrast from the particles. This can be used as it is as a further contrast mechanism or can be numerically integrated to determine the phase image and thus the complex wave field (allowing for example refocusing). [Explanation of symbols]

[0130] 1 First wave field intensity map 2 Second wave field intensity map 3. Lateral Phase Gradient Map 4. Target 5. Filters 6 Electromagnetic radiation sources 7. Electromagnetic Radiation Detectors 8 Objective Lenses 9 Tube Lens 10 Optical axis 11 Imaging system 12 Computer Processing Configuration 13. Computer Processors 14. Memory 15 Display S1~S3 Method steps

Claims

1. 1. A method for obtaining a transverse phase gradient of a wave field from at least a first wave field intensity map (1) and a second wave field intensity map (2), comprising: - capturing said first wave field intensity map (1) of the target (4) with a first incoherent gradient aberration using a first filter (5) having an attenuation profile with continuous derivatives, positioned between an electromagnetic radiation source (6) and an electromagnetic radiation detector (7) capturing said first wave field intensity map (1); capturing the second wave field intensity map (2) of the target (4) with a second incoherent gradient aberration using a second filter (5) with an attenuation profile having continuous derivatives, the second filter being positioned between an electromagnetic radiation source and an electromagnetic radiation detector capturing the second wave field intensity map, the second incoherent gradient aberration being different from the first incoherent gradient aberration; determining the transverse phase gradient based on the difference in logarithms of wave field intensity maps divided by the magnitude of the difference between at least the first incoherent gradient aberration and the second incoherent gradient aberration; A method comprising:

2. 2. The method of claim 1, wherein the difference between the first incoherent gradient aberration and the second incoherent gradient aberration is achieved by geometrically modifying one or more of the electromagnetic radiation source, the target, and the first filter and / or the second filter.

3. 3. The method of claim 2, wherein the geometrically modifying comprises modifying one or more of an illumination angle of the target, a lateral displacement of the first filter and / or the second filter, and a lateral displacement of the target.

4. 2. The method of claim 1 , wherein the electromagnetic radiation source used in capturing the first wave field intensity map is a first electromagnetic radiation source and the electromagnetic radiation source used in capturing the second wave field intensity map is a second electromagnetic radiation source, the second electromagnetic radiation source being displaced relative to the first electromagnetic radiation source.

5. The method according to any one of claims 1 to 4, wherein the first filter and / or the second filter are Gaussian filters.

6. The method according to any one of claims 1 to 4, wherein the first filter and / or the second filter are positioned between the target and the electromagnetic radiation detector.

7. The method of any one of claims 1 to 4, wherein the first filter and the second filter are the same filter.

8. The method of any one of claims 1 to 4, wherein the first filter and the second filter are different filters.

9. The step of obtaining the phase gradient may include the following steps: [Equation 1] where I １ (x １ , y １ ) is the position (x １ , y １ ) is the intensity of the first wave field intensity map at I ２ (x １ , y １ ) is the position (x １ , y １ ) and |τ １２ The method of any one of claims 1 to 4, wherein | is the magnitude of the difference between the first slope and the second slope.

10. The intensity I １ and the intensity I ２ 10. The method of claim 9, wherein {right arrow over (x)} represents the intensity of corresponding pixels in the first wave field strength map and the second wave field strength map.

11. The method of any one of claims 1 to 4, wherein the electromagnetic radiation detector comprises a camera.

12. 5. The method of claim 1, wherein the electromagnetic radiation detector used to capture the first wave field intensity map and the electromagnetic radiation detector used to capture the second wave field intensity map are the same electromagnetic radiation detector.

13. The method of any one of claims 1 to 4, wherein the attenuation profiles of the first and second filters have variable continuous derivatives.

14. The method according to any one of claims 1 to 4, wherein the attenuation profiles of the first and second filters have constant continuous derivatives.

15. 1. An imaging system, comprising: a source of electromagnetic radiation; an electromagnetic radiation detector; one or more filters with an attenuation having continuous derivatives, positioned between said electromagnetic radiation source and said electromagnetic radiation detector; a computer processor; a memory containing computer-implemented instructions that, when executed by said computer processor, perform the steps of the method of any one of claims 1 to 4; and configured to be adjustable between a first tilt degree and a second tilt degree.

16. 16. The imaging system of claim 15, wherein the one or more filters have an attenuation profile with a variable continuous derivative.

17. The imaging system of claim 15 , wherein the one or more filters have an attenuation profile with constant continuous derivatives.

18. A computer program product comprising instructions, which when executed by a computer processor of an imaging system, cause the computer processor to perform the steps of the method of any one of claims 1 to 4.

19. Use of the method according to any one of claims 1 to 4 or the imaging system according to claim 15 for contrast enhancement and / or digital refocusing.

Images