Method and apparatus for measuring a height map of a surface of a three-dimensional object using axial scan and modulated light

Abstract

The method for measuring a height map of a surface of a three-dimensional object using light comprises varying a distance between an optical focus position of an imaging system and the object being measured; applying a modulation to the light used to illuminate and image the object, obtaining a light modulation; acquiring at least one image, each exposed during a variation of the distance and the light modulation; determining a numerical value metric in at least one image pixel that is sensitive to the distance and to the light modulation; and determining a height map of the object from the numerical value metric, the light modulation, and the variation of the distance. An apparatus for carrying out steps of said method is also provided.

Description

[0001] METHOD AND APPARATUS FOR MEASURING A HEIGHT MAP OF A SURFACE OF A THREE-DIMENSIONAL OBJECT USING AXIAL SCAN AND MODULATED LIGHT

[0002] BACKGROUND

[0003] Topographic optical imaging at the microscale plays a crucial role in industrial and scientific processes, as disclosed by Zuo, C. et al. Deep learning in optical metrology: a review. Light: Science and Applications 11, (Springer US, 2022), and also in Chen, B. C. et al., Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution. Science 346, (2014).

[0004] Examples of topographic optical imaging applications include optical inspection in production lines. Reference is made herein, for example, to Ebayyeh, A. A. R. M. A.

[0005] & Mousavi, A., A Review and Analysis of Automatic Optical Inspection and Quality Monitoring Methods in Electronics Industry. IEEE Access 8, 183192-183271 (2020).

[0006] Still further examples of topographic optical imaging at the microscale are metrology of additively manufactured parts, as disclosed by Vilar, N. et al. Optical system for the measurement of the surface topography of additively manufactured parts. Meas. Sci. Technol. 33, 104001 (2022), and also three-dimensional (3D) surface measurement of biomaterials as disclosed by Marrugo, A. G., Gao, F. & Zhang, S. State-of-the-art active optical techniques for three-dimensional surface metrology: a review. J. Opt. Soc. Am. A 37, B60 (2020).

[0007] Topography maps are typically reconstructed from a z-stack, that is, a collection of images from different focal planes acquired sequentially, as in confocal microscopy; see for example Ji, N., Freeman, J. & Smith, S. L. Technologies for imaging neural activity in large volumes. Nat. Neurosci. 19, 1154-1164 (2016).

[0008] Said process for reconstructing topography maps through collection of images from different focal planes acquired sequentially may be slow, in particular for bulky objects that require large mechanical displacements between focus and object. The problem can be further aggravated when pursuing sub-micrometric optical resolution. In this case, high numerical aperture (NA) optics are needed which feature a short depth-of-field, and consequently, require a large number of z-planes for proper reconstruction. As a result, commercial surface microscopes are ill-suited for characterizing fast moving industrial processes or rapidly evolving biological systems. Several strategies have been developed to reduce acquisition time in topographic imaging. They can be broadly classified into two main groups.

[0009] A first group of strategies consists of techniques aimed at speeding up the assembly of a z-stack. One example includes spatiotemporal multiplexing as disclosed by Cheng, A., Gongalves, J. T., Golshani, P., Arisaka, K. & Portera-Cailliau, C.

[0010] Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing. Nat. Methods 8, 139-142 (2011).

[0011] Further examples of said first group of strategies seeking to reduce acquisition time in topographic imaging are multi-focus microscopy as reported by Abrahamsson, S. et al. in Fast multicolor 3D imaging using aberration-corrected multifocus microscopy. Nat. Methods 10, 60-3 (2013), and also by Beaulieu, D. R., Davison, I. G., Kihg, K., Bifano, T. G. & Mertz, J., Simultaneous multiplane imaging with reverberation two- photon microscopy. Nat. Methods 17, 283-286 (2020).

[0012] Encoded illumination methods are also another example of said first group of strategies to reduce acquisition time in topographic imaging. For example, He, H. et al. in Tomographic-Encoded Multiphoton Microscopy. ACS Photonics (2022). doi: 10.1021 / acsphotonics.2c00629, and Zunino, A. et al. in Multiplane Encoded Light- Sheet Microscopy for Enhanced 3D Imaging, ACS Photonics (2021). doi : 10.1021 / acsphotonics.1c01401 , and Ren, Y. X. et al in. Parallelized volumetric fluorescence microscopy with a reconfigurable coded incoherent light-sheet array. Light Sci. Appl. 9, (2020) disclose encoded illumination methods.

[0013] The use of variable optical elements for fast focus control has been also provided as disclosed by Kang, S. K., Duocastella, M. & Arnold, C. B. Variable Optical Elements for Fast Focus Control. Nat Phot. 14, 533-542 (2020).

[0014] While the above approaches in said strategies to reduce acquisition time in topographic imaging have been shown to be capable of retrieving 3D information from a sample in real-time, they have been found to provide a limited axial range, little ease of use, high cost of implementation, or limited range of samples that can be characterized. Alternatively, a second group of strategies to reduce acquisition time in topographic imaging is based on reducing the information necessary for 3D image reconstruction. This is achieved by exploiting the intrinsic sparsity of most common samples. One example of such approach is to reduce the scanned volume by selecting predefined regions in a sample, as in random scanning microscopy. This is disclosed, for example, by Nadella, K. M. N. S. et al. in Random-access scanning microscopy for 3D imaging in awake behaving animals. Nat. Methods 13, 1001-1004 (2016). However, the information required a priori is not generally accessible.

[0015] Instead, computational approaches have been provided such as compressed sensing enabling full topographic reconstruction from far fewer images, up to one order of magnitude, than traditional z-stacks as disclosed in Edgar, M. P., Gibson, G. M. & Padgett, M. J. Principles and prospects for single-pixel imaging. Nat. Photonics 13, 13-20 (2019).

[0016] Still, the gain in 3D imaging speed can come at the cost of reconstruction fidelity. Said techniques are also computationally expensive, typically requiring off-line processing, as reported by Gao, L., Liang, J., Li, C. & Wang, L. V. Single-shot compressed ultrafast photography at one hundred billion frames per second. Nature 516, 74-77 (2014).

[0017] A need therefore still remains for real-time topographic optical imaging of large volumes at the microscale.

[0018] SUMMARY

[0019] A method is provided herein for measuring a height map of a surface of a three- dimensional object using light with which the above need is satisfied while further providing a number of significant advantages.

[0020] The strategy behind the present method is a new scanning model that does not follow traditional sequential plane-by-plane scan methods.

[0021] The present method steps are not limited to the order in which they are recited herein.

[0022] The present method comprises a step of varying a distance between an optical focus position of an imaging system and the object being measured. Said step may be performed by one or more of moving one of the object and the imaging system relative to each other; changing the optical focus position of the imaging system; and modifying the wavelength of the illumination light.

[0023] The method further comprises a step of applying a modulation to the light used to illuminate and image the object, obtaining a light modulation.

[0024] A step is also performed for acquiring at least one image, each exposed during a variation of the distance and the light modulation.

[0025] A further step is performed to determine a numerical value metric in at least one image pixel that is sensitive to the distance and to the light modulation.

[0026] The method further comprises a step of determining a height map of the object from the numerical value metric, the light modulation, and the variation of the distance. A height value is thus determined from the numerical value metric from one or more images, the light modulation applied during the acquisition to said images, and the variation of the distance applied during the acquisition of said images. The height map of the object is obtained by repeating the determination of said height value for a plurality of image pixels.

[0027] The above mentioned metric may be based on at least one of detection of structured light in the acquired image, detection of an object surface texture, applying a spatial mathematical operator to the image sensitive to structured light or to the object surface texture, a signal from a confocal system, and a signal from an interferometer.

[0028] The determined height map may be reconstructed using at least one of applying light modulation and decoding a discrete height map, applying light modulation and obtaining a continuous height map.

[0029] On the other hand, the light modulation may be performed by one or more of varying light intensity, light wavelength, light polarization state, turning on and off the illumination, and combining and varying a relative intensity of a plurality of light sources having different properties.

[0030] Furthermore, the light modulation may be performed through light intensity modulation implemented with a finite number of intensity levels in a given sequence that is unique for each image, forming a code that identifies a set of values for the distance. In some cases, the light modulation may be implemented with two intensity levels, in which case the sequence forms a binary code that codes the set of values for the distance. In other cases, the light modulation may be performed through light intensity modulation implemented with at least one of: a sequence of light pulses, a sinusoidal function, a sawtooth function, a square wave function, and any combination of the previous with different time delays.

[0031] In some cases, the method may be implemented using an interferometer as the imaging system, the optical signal of the interferometer as the numerical value metric, and the light modulation is periodic with a period corresponding to the time required to vary the distance an amount equivalent to a multiple of half the wavelength of the illumination light.

[0032] In some cases, the method may be implemented using a plurality of illumination systems employing structured light with dissimilar patterns, and such that they may be independently modulated in time.

[0033] In some cases, the method may be implemented using an imaging system having a longitudinal chromatic optical aberration, and using an illumination system capable of modulating the wavelength of the illumination light or having a plurality of illumination systems with different wavelengths. In this cases, the variation of the wavelength is equivalent to varying the distance between the optical focus position and the object.

[0034] With the method disclosed herein above, only a reduced set of images is required to reconstruct the height map of the object. Each image is acquired during a focal sweep through an axial range, due to the implemented variation of the distance. The range of axial distances covered by each image defines the measurement range and, together with the lateral field-of-view of the imaging system, defines the measured volume. Synchronized time-modulated illumination is employed during the acquisition of each image such that information about the axial location of the sample can be encoded in each image. As a result, strong data sparsity inherent in three- dimensional topographic imaging can be exploited, enabling the axial localization of the object with order-of-magnitude improvements in acquisition time.

[0035] The present method enables fast 3D topographic imaging. Examples of reconstructed topographies using one example of implementation of the method as described below, include measurements of surfaces spanning 100 pm in axial range from only eight images with sub-micrometre resolution. Such 3D topographic imaging can be performed at speeds not possible in prior art methods known so far.

[0036] By contrast, the conventional approach for determining the axial position of an object to be measured is by scanning an axial range into N planes and interrogating all the planes. Within the meaning of the present disclosure, interrogation refers to inferring whether the object is or is not present at a given sampling plane, within an axial margin equivalent to the depth of field of the imaging system, where the depth of field is the axial range of distances that a plane may be considered to be in focus. Since each sampling plane corresponds to an image, at least / V images are typically required. The number of images / V depends on the a priori information of the sample to be measured, the properties of the optical system, and the scanning range. However, the number of images / V is typically large.

[0037] The present method allows to determine an axial position of an object to be measured with a reduced set of images. An exemplary basic form of the present method may be based on a binary search of the sample, in which merged groups of planes are interrogated and it is checked whether the sample is or is not present in each group of planes. Such implementation advantageously enables a dramatic reduction in the number of queries, and therefore the number of images. In the case of implementation of a binary search, the axial position of the sample can be determined by using only Iog2( / V) images. As a result, information is extracted with far fewer samples / images through the present method than through known methods based on sequential plane-by-plane scan.

[0038] Implementation of the method in a form of a binary search involves acquiring a set of images while the optical focus is scanned through the entire measurement range. Information from the in-focus plane and all other planes is therefore merged onto each image. The axial location of the in-focus plane is unknown, as it depends on the height of the sample, and constitutes the measurand. During the focal sweep the illumination is turned on and off with a precisely controlled sequence that is different and unique for each image. Interrogation of each image to infer whether the object is present at the group of axial positions defined by the illumination during the focal sweep is performed by calculating the numerical value metric, which is sensitive to the presence of the object close to the optical focus position. Determination of the height of the object at each pixel where the metric is calculated amounts to determining a height map of the object.

[0039] In such binary implementation of the method the illumination has two states and the sequence implemented during the acquisition of each image determines a binary code. Therefore, obtaining and binarizing values of the metric for each image amounts to obtaining the code that identifies the height of the object. With such binary approach, the measurement range is divided in a discrete set of values of the distance, each identified by the code. Decoding therefore provides the value of the distance within the discrete set of values that corresponds with the height of the object. It is also possible to implement a code with more than two states. Alternatively, the modulation of the light may also be varied in a continuous fashion, and furthermore it may be continuous and periodic. Obtaining the height of the object in this case is not limited by the discretization of the illumination sequence.

[0040] An apparatus for measuring a height map of a surface of a three-dimensional object using light through the above method is also disclosed herein.

[0041] The present apparatus comprises an imaging system defining an optical focus position. Said imaging system may comprise at least one of a microscope system, at least one camera, at least one polarized camera, at least one hyperspectral camera, a point-scanning system, at least one polarization-sensitive detector, and at least one hyperspectral detector.

[0042] The apparatus further includes a system to vary a distance between the optical focus position of the imaging system and the object being measured. Said system may be based on the mechanical movement of the object or of the imaging system, providing a relative movement. Said system may also be based on changing the optical focus position of the imaging system. Changing the optical focus position of the imaging system may be accomplished, for example, by moving of one or more individual optical elements of the imaging system, or by incorporating a variable optical element such as a focus-variable lens.

[0043] One or more illumination systems are also provided to illuminate the object being measured. Said illumination system(s) may be configured to project structured light on the object. A system is also included to apply a modulation to the light used to illuminate and image the object. Each system may function independently from each other. One or more detectors may be provided for acquiring one or more images. The structured light projected on the object may be independently modulated.

[0044] The above mentioned imaging system may be, for example, an interferometer and the light modulation is periodic with a period corresponding to the time required to vary the optical focus position a distance equivalent to a multiple of half the wavelength of the illumination light.

[0045] The above mentioned imaging system may be, for example, a confocal imaging system.

[0046] The illumination system may comprise at least one of a system to change the state of polarization of the light, and a system to change the wavelength of the light used for illumination.

[0047] The apparatus may include at least one of a system to determine the numerical value metric and a system for reconstructing the height map of the object.

[0048] BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Non-limiting examples of the present disclosure will be described in the following, with reference to the appended drawings, in which:

[0050] Figure 1 diagrammatically shows one example of an apparatus 1000 for implementing the present method;

[0051] Figure 2 shows a graph of a focus-sensitive signal S obtained through a metric based on the magnitude of the Laplacian of the image field via Equation (2) plotted for two selected pixels across a measurement range;

[0052] Figure 3 includes graphs where a set of images / / with coding sequences M, are acquired through conventional scanning;

[0053] Figure 4 is a graph where signal S is sampled through conventional scanning as in figure 3;

[0054] Figure 5 includes graphs of coding sequences Mi corresponding to a set of images / , acquired according to the present method, implementing a binary code based on a Gray code;

[0055] Figures 6 and 7 are graphs of integrated signals S3 and S4 respectively, for one pixel with height zs, showing how they respond to the presence of the sample;

[0056] Figure 8 are graphs of intensity modulated illumination, where three images are acquired with sinusoidal modulation and with 2TT / 3 relative phase shift;

[0057] Figure 9 shows one example of an apparatus for implementing the present method; and

[0058] Figure 10 shows height map measurements using an apparatus according to Figure 9, of (a) a titled mirror, (b) a region of a coin containing a star shape, and (c) a region of a material measure NPL B40 type AIR as defined in ISO 25178-70:2014 Geometrical product specification (GPS) - Surface texture: Areal - Part 70: Material measures (Vernier, Geneva, Switzerland: International Organization for Standardization).

[0059] DETAILED DESCRIPTION OF ONE EXAMPLE IMPLEMENTATION

[0060] One non-limiting example of an apparatus 1000 for measuring a height map of a surface of a three-dimensional object or sample 100 using light is disclosed herein and illustrated in figures 1 and 9 of the drawings. The apparatus 1000 is configured for performing the present method for measuring a height map of the object 100 using light.

[0061] The apparatus 1000 in the example shown is of the confocal type and comprises an imaging system 200 with a defined optical focus position whose field of view and axial measurement range define a volume of interest containing the sample to be measured 100, at least one illumination system 400, a light modulation system 700, a system to vary the distance 600, a detector 500, and a system to reconstruct the height of the object 800;

[0062] The present apparatus 1000 is configured to perform the steps of the present method for determining an axial position of the object being measured 100. In prior art plane-by-plane scan methods, the measurement range is divided in a number / V of equally spaced planes and the measured object is scanned axially whilst measuring or calculating a signal at each plane, building an axial response for each image pixel. Localization of the maximum of the axial response amounts to measuring the height at a given pixel. This process resembles performing a linear search, where a large number of images / V is required involving a search of / V steps, that is the axial sampling of the axial response, where each image represents a query that interrogates the presence of the object at each plane. By contrast, with the present method, the axial position of the object 100 for a given image pixel can be determined with far fewer measurements enabling fast reconstruction of topography maps. Reduction of the number of queries provides a commensurate reduction of the number of images. In the present method, instead of sampling the axial responses in a plane-by-plane fashion, each measurement collects information from merged groups of planes, and therefore interrogation of each image enables to check whether the object 100 is or is not in the corresponding group of planes. One way of designating the groups of planes is to implement a binary code through the entire axial measurement range. In the case that the code implements a binary search, only Iog2( / V) images are required for determining what axial plane contains the axial position of the object 100. / V is typically a large number, so the present method provides a great reduction of the number of images required to measure a height map of the object.

[0063] Extracting information using far fewer samples / images as compared with prior art methods is extremely advantageous for real-time topographic optical imaging of large volumes at the microscale. For example, using a Gray code as encoding sequence Mj as shown in figure 5, if a measurement range of interest Az of 400 pm is sampled conventionally at steps of 1 .6 pm as in prior art methods, 250 images would be required, whereas the present method provides equivalent axial localisation using only 8 images.

[0064] The relative strength of the focus-sensitive signal combined with a continuous modulation of the light can be used to calculate the axial location of the object 100 with increased accuracy, as shown in figure 8, as explained below.

[0065] As shown in figure 1 , illumination light 300 is projected on the object 100 through said illumination system 400. Illumination light 300 is, in the example shown, temporally coded illumination 300 to illuminate the object being measured 100. Furthermore, the illumination system 400 may be configured to project structured light 300. Structured illumination may be implemented using a transmissive chrome-on-glass mask with a checker-board pattern, which is projected onto the object 100.

[0066] A system to apply a modulation to the illumination light 300 used to illuminate and image the object 100 as well as one or more detectors 500 for acquiring one or more images are also provided. Acquired images are exposed during a variation of the distance and the light modulation. The images are acquired while the optical focus is scanned through the entire measurement range Hz. Information from the in-focus plane and all other planes is therefore merged onto each image. The axial location of the in-focus plane is unknown, as it depends on a height zsof the object 100 and constitutes the measurand. In an implementation where light modulation is performed by varying the intensity of the illumination light in two intensity levels and one intensity level is zero, the illumination 300 is turned on and off during the exposure with a sequence that is different and unique for each image.

[0067] In the example described herein, a system to determine the numerical value metric in at least one image pixel that is sensitive to the distance and to the light modulation is provided. Said metric may be based on at least one of detection of structured light in the acquired image, detection of an object surface texture, applying a spatial mathematical operator to the image sensitive to structured light or to the object surface texture, a signal from a confocal system, and a signal from an interferometer.

[0068] From said numerical value metric, the light modulation, and the variation of the distance, a height map of the object 100 is also determined. Examples of height map measurements using an apparatus according to figure 9 are shown in the graphs illustrated in figures 10a, 10b, and 10c of the drawings.

[0069] The apparatus 1000 further includes a system for reconstructing the height map of the object 100. By means of said height map reconstructing system, said determined height map may be reconstructed. The reconstructing system may be based on using at least one of applying light modulation and decoding a discrete height map, applying light modulation, and obtaining a continuous height map.

[0070] The example implementation of the present method herein described is based on a Gray code for the axial encoding of the focus-sensitive signal, S / . Such code is used as encoding binary sequence M, to calculate a step number d that contains a height of the object, zs, as illustrated in figure 5 of the drawings. In this example, the illumination is turned on and off according to the binary values of the sequence Mi.

[0071] For a given illumination sequence Mj(z), the acquired image I(x, y, Mi) acquired whilst the distance between the object and the optical focus is varied through the measurement range is:

[0072] Zmax and Zmin is the measurement range, r (x,y) is the reflectivity of the object or sample, L(x,y) is the illumination of the sample plane, PSF is the imaging point-spread function, zsis the height of the object at location (x,y) that we intend to measure, * denotes two-dimensional convolution in the tangential plane (x,y).

[0073] The focal sweep is assumed to be implemented in a constant velocity v through the measurement range zlzand therefore z can be based on time such as z = v t. However, any other relation z(f) would be applicable as long as it is known and monotonic. It is to be noted that with this binary implementation it is not possible to infer the location of the in-focus plane from a single focal-sweep image. However, a signal from the image that is focus sensitive can be calculated, thereby calculating a numerical value metric. Based on the value of the metric it would be therefore possible to detect whether, during focal sweep, illumination was on or off at the time where the object 100 was in-focus.

[0074] One option for the numerical value metric that implements a focus-sensitive signal, is the detection of high spatial-frequency content in the image. Such content can be originated either from the sample reflectivity spatial map r(x,y) or from the illumination pattern L(x,y). This is a focus-sensitive signal since high spatial-frequency features are only recorded if M, {z = zs) 0 because PSF(x, y, z-zs) acts as a strong low-pass filter for z zs(within depth of field). As an example, a metric based on the magnitude of the Laplacian of the image field provides such signal, as shown in figure 2: denotes spatial Gaussian filtering with standard deviation o, included for suppressing noise and smoothing. Figures 6 and 7 show illustrations of integrated signals S3 and S4 respectively, for one pixel with height zs, showing how they respond to the presence of the object 100. Although signals, S3, S4, are for one pixel with height zs, results are calculated in parallel for all pixels.

[0075] The above information is exploited in the present method. Through a simple threshold on S((x,y) the presence or absence of the object 100 is detected at any of the locations masked axially by the binary modulation Mi(z). As an example, if M,(z) = 1 is implemented for z < (zmax - zmin) / 2 and Mj(z) = 0 otherwise, a value of S / (x, y) above or below the set threshold would indicate that the height of the object 100 at (x, y) is somewhere in the first or second half of the measurement range Az. The combination of a few images with an appropriately designed set of sequences in conjunction with the assumption that the object 100 is topographic, can therefore be used to perform an axial search of the height at each pixel. That is, if the measurement range Az is divided in N steps of size T = (zmax - zmin) / , the step number d corresponding with the height of the object 100 at each pixel can be found.

[0076] If encoding sequences M, implement a basic binary code, then the step number d that contains the axial location of the object at any lateral location within the captured field of view may be inferred through Equation (3) as follows: d(x,y) = ' i=-l2(n~i)H(Si(x,y) - 5th(x,y)) (3) where n is the number of sequences / images,

[0077] / - / (■) is the Heaviside step function used to binarise the field Sj(x,y), and Sth (x, y) is a calibrated threshold over which the object is deemed detected.

[0078] For any other coding sequence, such as a Gray code as stated above, a decoding step precedes determination of the step number d. Figure 5 shows one example where a set of images / / with coding sequences M, are acquired according to the present method implementing a Gray code with n = 4 images. Calculation of the numerical value metric provides the focus-sensitive signal S / and binarization of the focus-sensitive signal S / provides a Gray code to calculate step number d containing the height zsof the object 100. As stated above, in prior art methods based on conventional scanning as shown in figure 3 wherein h ... Indesignates image acquisition and Si... Sndesignates optical sectioning, the signal is sampled with a uniform sampling rate as illustrated in figure 4, requiring a large number of samples / images as compared to the method herein described.

[0079] The minimum height of the axial step that can meaningfully be implemented in the present method, using a binary encoding sequence is dictated by the depth-of- field of the imaging system, as it determines the ability to resolve axially the detection of presence or absence of the object 100. Implementing smaller steps would not yield increased axial resolution, due to the convolution in Equation (1). However, it is possible to further exploit the prior knowledge of sparsity to maximise localisation precision. This may be carried out by extracting information from the continuous variation of the numerical value metric as a function of the object height. As an example, this can be implemented by modulating the intensity of the illumination in time. Also this can be implemented using pulsed illumination and exploiting the axial response of Equation (1). A particular example, implemented using sinusoidally- modulated illumination, is to acquire three images with 2TT / 3 relative phase shift. The relative strength of the focus-sensitive signal can be used to calculate the axial location of the object 100 with increased accuracy.

[0080] If the time-modulated intensity is chosen to follow a periodic function, calculation of the object height will be restricted to the height associated with the period of the illumination, effectively reconstructing a height map that is wrapped at steps equivalent to the illumination period, as: zs(x,y) = zs(x,y) - floor(zs(x,y) / zp(4) wherein zs(x,y) is the reconstructed, wrapped height, zs is the object height, zpis the scanning height associated with the period time of the periodic illumination, and the floor() function returns the largest integer that does not exceed its argument.

[0081] An interesting implementation of the present method combines the examples described to calculate a wrapped height map, in combination of an implementation of a binary sequence designed to be used to provide a means for unwrapping the height map. For this, one option is to implement each focal-sweep image with an illumination intensity modulated sinusoidally in time and with N cycles through the measurement range Az, as illustrated by the example illustrated in figure 8. That is, the modulation at the second stage is set as follows: where 5j is a phase offset.

[0082] Since filtering in Equation (2) extracts high spatial frequency information, which is only present at planes close to zs, the magnitude of Sj(x,y) is proportional to / W7(z =zs), where Smax(x,y) is the value of the signal in Equation (2) when Mj(z) = 1 , with m being the resulting reduction in contrast that appears due to the depth of field of the imaging system.

[0083] By repeating the measurement with different phase shift 5j it is possible to solve for the axial location of the object 100. As an example, implementing a set of phase shifts 8j = {— 2TT / 3, 0, 2TT / 3] the axial location of the object 100 can be readily determined as follows: where arg( ) is the argument of a complex number in the range [0,2TT) and i = — 1. This is illustrated in figure 8 wherein case, h... Indesignates image acquisition and Sv... Sndesignates optical sectioning. Other algorithms and variations that work with different number of images and relative phase shifts would be equally applicable to the present method. The result of Equation (7) is the topography of the object 100 wrapped at steps of our illumination cycle. As mentioned, combination of the method with the results from implementation of a binary sequence, shown in the example illustrated in figure 5, provides a mechanism for performing a robust and unambiguous unwrapping, as: zs(x, y ) = zmin+ d • T + zs(x, y ) (8) where d is the step number obtained binary-sequence implementation.

[0084] For a robust simultaneous determination of the step number d and the wrapped measurement ^, results from the experimental implementations included here implement a Gray code using an additional image (corresponding to a higher frequency) in the stage of the binary sequence implementation of the present method, whereas the stage of the intensity-modulated sequence implementation of the periodic illumination with a set of phase shifts of 8j = {0, TT / 2, n, 3TT / 2, 2TT] is implemented.

[0085] Figure 9 diagrammatically shows one example of an experimental apparatus that implements the present method. The apparatus 1000 includes an imaging system based on a microscope objective and a tube lens, an illumination system including LED illumination and a means for projecting structured light, a light modulation system, and a means to vary a distance between the optical focus position of the imaging system 200 and the object being measured 100. In this non-limiting example, this is carried out by means of a motorized linear stage configured to move a microscope objective relative to the object 100. A measurement range Az is set to 100pm. The motorized stage provides a suitable movement speed and camera exposure time is correspondingly set so that the object 100 is moved at constant velocity through the measurement range Az during the exposure time. A 20x / 0.45NA objective is employed in this example with a depth of field of about 2.6 pm.

[0086] Measurement range Az can therefore be divided into approximately N = 40 steps, so that the maximum number of binary-modulated images is 7, as is the lowest integer satisfying 2n-1> 40. However, it is not necessary to implement as many images. In this case the measurement range Az is divided using N = 8 steps, with a step size of T = 12.5 pm. Furthermore, continuous and periodic illumination based on a sinusoidally- modulated intensity has been implemented such that a period corresponds to the step size T. The illumination system 400 includes a 532 nm central wavelength Light Emitting Diode (LED) that can be readily controlled and synchronized with the acquisition. The illumination system employs structured light in the form of a checkerboard pattern, implemented using a transmissive mask included in the illumination light path. Examples of reconstructed height maps implemented with the method herein described are shown in Figure 10.

[0087] Although only one example of implementation has been disclosed herein, other alternatives, modifications, uses and / or equivalents thereof are possible. The signal to be measured may be any signal that is focus-sensitive, such as a focus variation operator, a confocal signal, etc. Different hardware to physically scan the object 100 may be used, including a motorised or piezo-electric stage. Remote focusing techniques may be used for remotely controlling the focal position. Tuneable optics may be also used to implement the present method. Remote focusing, tuneable optics or equivalent methods may be beneficial for speed as they provide for faster operation since physical inertia involved in relative movement of the object 100 and the hardware may be avoided. All possible combinations of the described examples are also thus covered. The scope of the present disclosure should not be limited by particular examples but should be determined only by a fair reading of the claims that follow. Reference signs related to drawings placed in parentheses in a claim are solely for attempting to increase the intelligibility of the claim and shall not be construed as limiting the scope of the claim.

Claims

CLAIMS1. A method for measuring a height map of a surface of a three-dimensional object using light, the method comprising:- varying a distance between an optical focus position of an imaging system and the object being measured;- applying a modulation to the light used to illuminate and image the object, obtaining a light modulation;- acquiring at least one image, each exposed during a variation of the distance and the light modulation;- determining a numerical value metric in at least one image pixel that is sensitive to the distance and to the light modulation; and- determining a height map of the object from the numerical value metric, the light modulation, and the variation of the distance.

2. The method of claim 1, wherein the variation of the distance is performed by one or more of:- moving one of the object and the imaging system relative to each other;- changing the optical focus position of the imaging system; and- modifying the wavelength of the illumination light.

3. The method of any preceding claim, wherein the light modulation is performed by one or more of:- varying light intensity;- varying light wavelength;- varying light polarisation state;- turning on and off illumination; and- combining and varying a relative intensity of a plurality of light sources having different properties.

4. The method of any preceding claim, wherein the light modulation is performed through light intensity modulation implemented with a finite number of intensity levels in a given sequence that is unique for each image, forming a code that identifies a set of values for the distance.

5. The method of claim 4, wherein the light modulation is implemented with two intensity levels, forming a binary code.

6. The method of any of the claims 1-4, wherein the light modulation is performed through light intensity modulation implemented with at least one of:- a sequence of light pulses;- a sinusoidal function;- a sawtooth function;- a square wave function, and- a combination of the previous with different time delays.

7. The method of any preceding claim, wherein the metric is based on at least one of:- detection of structured light in the acquired image;- detection of an object surface texture;- applying a spatial mathematical operator to the image sensitive to structured light or to the object surface texture;- a signal from a confocal system; and- a signal from an interferometer.

8. The method of any of the preceding claims, wherein the determined height map is reconstructed using at least one of:- applying light modulation and decoding a discrete height map;- applying light modulation and obtaining a continuous height map.

9. An apparatus for measuring a height map of a surface of a three-dimensional object using light, according to the method of any of the claims 1-8, the apparatus comprising:- an imaging system defining an optical focus position;- a system to vary a distance between the optical focus position of the imaging system and the object being measured;- one or more illumination systems to illuminate the object;- a system to apply a modulation to the light used to illuminate and image theobject; and- one or more detectors for acquiring one or more images.

10. The apparatus of claim 9, wherein the illumination system is configured to project structured light on the object.

11. The apparatus of claim 9, wherein the imaging system is an interferometer and the light modulation is periodic with a period corresponding to the time required to vary the optical focus position a distance equivalent to a multiple of half the wavelength of the illumination light.

12. The apparatus of any of the claims 9-11, wherein the imaging system comprises at least one of:- a microscope system;- a camera;- a polarized camera;- a hyperspectral camera;- a point-scanning system;- a polarization-sensitive detector; and- a hyperspectral detector.

13. The apparatus of any of the claims 9-12, wherein the illumination system comprises at least one of:- a system to change the state of polarization of the light; and- a system to change the wavelength of the light used for illumination.

14. The apparatus of any of the claims 9-13, wherein it includes a system to determine the numerical value metric.

15. The apparatus of any of the claims 9-14, wherein it includes a system for reconstructing the height map of the object.

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