1. Introduction

Optical metrology plays a vital role in quality assurance of micro parts [1,2]. Especially mechanical and electrical components with dimensions in the micrometer range are essential in everyday modern applications, such as mobile phones, cars and medical devices. Since their proper operation is vital for the correct and reliable function of the system they are part of, a particularly low failure rate in the ppm range is often required. This calls for optical metrology that can provide fast and high precision form measurement directly in the production environment [3].

White light interferometry (WLI) is a well established technique for optical inspection of micro parts. It combines a large ambiguity range [4,5] with measurement uncertainties in the range of the surface roughness [6], even down to nanometers in case of specular surfaces. A white light interferometer splits partially coherent light into an object wave and a reference wave. While the object wave is scattered by the surface under test (SUT), the reference wave is reflected by a mirror (reference surface). Upon recombination of the light across a camera sensor, an interference pattern is registered only for those areas of the SUT, where the distance between camera and surface matches the distance between camera and reference mirror within the range of the coherence length. The profile of the surface can then be determined by moving the reference mirror and the imaging system along the optical axis.

Even though scanning WLI is widely accepted as an industry standard for quality inspection, the main drawbacks of the technique are its sensitivity to environmental disturbances and the large number of required recordings due to the mechanical scanning approach [7]. In many cases, these disadvantages prevent it from being integrated directly into a production line. In other implementations, the mechanical movement is therefore replaced by a spectral sampling technique [8] using a swept source [9] or diffractive elements [10]. While spectral domain WLI solves the problem of the mechanical scanning, the height range of currently available methods is fundamentally limited by the corresponding depth-of-focus (DoF) of the imaging system, which is often unacceptable in microscopic applications.

In digital holography (DH), light reflected or scattered by the SUT is superposed with a coherent reference wave [11,12]. The recorded interference pattern is referred to as the digital hologram. If the properties of the reference wave are known, DH allows numerical propagation of the object wave and therefore enables digital volumetric imaging [13] and refocusing [14,15] subsequent to the recording process. Recently, spectral holography has gained some attention, with applications to laser pulse analysis [16], spectroscopy [17,18], reduction in phase noise [19–21] and enhancing the sectioning capabilities in the analysis of transparent objects [22]. Furthermore, we find a number of so called multi-$\lambda$ approaches for the purpose of surface profiling [23,24] or biomedical investigations [25]. Here, various digital holograms are recorded using different wavelengths and evaluated in combination. The evaluation typically focuses on the creation of synthetic (or artificial) wavelengths in order to avoid ambiguity problems [26]. However, because the evaluation is solely based on fully coherent phase values, it is susceptible to phase noise caused by out-of-focus parts, e.g., in microscopy, and typically has lower precision when compared to methods based on coherence scanning.

In this study we present Flash-Profilometry as a new coherence profiling method using spectral holography. The idea is to overcome the limitations of WLI and DH by numerically performing the process of coherence scanning throughout the profile of the object based on recording a set of digital holograms using different wavelengths without the need for any mechanically moving components.

The benefits of this approach are substantial: The corresponding measurement system provides results comparable to those of a scanning WLI. Yet, it does not require any imaging optics and thus does not suffer from lens aberrations, DoF limitations or spectral dispersion issues. It is lightweight and very compact, which means a significant advantage towards pick and place applications for example. Due to the spectral sampling, it requires far less recordings, which has the potential to reduce the measurement time by more than one order of magnitude as compared to a scanning WLI. Finally, spectral measurements can be numerically phase aligned (coupled) in post processing, thus the method is almost immune against rigid body movements and vibrations. In the following we will present the details of Flash-Profilometry based on spectral holography in section 2 along with its properties depending on the selection of wavelengths. Finally, in section 3., we present experimental results using a specular step surface, showing that the results are fully comparable to those of scanning WLI.

2. Methods

2.1 General concept

Figure 1 shows a sketch of the setup demonstrating the general concept. It consists of a Michelson-Interferometer with the object in one interferometer arm. Denoting the wave reflected by the object as $u$ and the wave travelling along the reference path as $r$, we can determine the intensity of the interference pattern in the recording plane by

 

Fig. 1. Sketch of the setup used for white light interferometry using spectral holography (Flash-Profilometry): The basic concept is a digital holographic recording arrangement based on a Michelson interferometer with the object placed in one interferometer arm. In its initial state, the $\delta _{0}$-plane located at $z_{2}$ has the same distance from the camera as the reference mirror, i.e., $z_{2}=-d_{0}$. Multiple digital holograms using different wavelengths are recorded to facilitate spectral sampling of the mutual coherence function in the camera domain, which is at its maximum for object light reflected from the $\delta _{0}$-plane. The concept is based on propagating the mutual coherence function from the camera domain to $z_{2}$ in order to focus those parts of the object for which $\vert \Gamma \vert$ is at its maximum. This process is then repeated for various distances $d_{0}+\Delta d$ of the mirror, which also shifts the position $z_{2} = -(d_{0}+\Delta d)$ of the $\delta _{0}$-plane through the object volume, thereby facilitating coherence scanning. However, the great benefit of the spectral sampling is that the mirror does not need to be mechanically shifted. Instead, the whole process can be performed numerically.

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2.1.1 Spectral sampling of the mutual coherence function

Let us assume the light having a power spectral density composed of a set of discrete spectral lines with frequencies $\nu _{n}$. This allows decomposing $u(\vec {x},z_{1};t)$ into its spectral modes $u_{n}$ by

Inserting Eq. (3) and Eq. (4) into Eq. (2) yields

By construction, the $\Gamma _{n}(\vec {x},z_{1})$ are the monochromatic spectral modes of the mutual coherence $\Gamma (\vec {x},z_{1})$. Spectral domain sampling has profound advantages. In fact, fully coherent light, emitted by a tunable laser source for instance, can be used to record the individual $\Gamma _{n}$. Subsequent to the measurement, we can numerically determine the result expected from using, e.g., a broad band light source, by a simple summation. This enables digital tailoring of coherence properties, including the creation of low temporal coherence, based on a set of fully coherent measurements, as will be discussed below in section 2.4.

2.1.2 Propagating the mutual coherence function

If we consider limited temporal coherence, $\vert \Gamma \vert$ will have its maximum for light which has been reflected or scattered from the $\delta _{0}$-plane in Fig. 1. However, it is not straight forward to associate $\Gamma$ with specific areas of the object, since the camera does not provide a focused image of the $\delta _{0}$-plane. We therefore need to propagate the mutual coherence into the $\delta _{0}$-plane based on its known appearance in the recording domain. To this end, we will introduce a method which allows calculating $\Gamma (\vec {x},z_{2})$ at any vertical position $z_{2}$ based on the measured spectral modes $\Gamma _{n}(\vec {x},z_{1})$ at position $z_{1}$. With reference to Eq. (5) we can write for the spectral modes at position $z_{2}$

Here, $\mathcal {F}\{ \cdots \}$ denotes the Fourier transform operation, $\hat {w} = \mathcal {F}\{ w \}$ and $k_{z}$ is the $z$-component of the wave vector $\vec {k}$. If we assume for example a plane reference wave with its origin located at the center of the beam splitter

Equation (10) enables the propagation of the mutual coherence in any plane parallel to the camera plane. The requirement is, that the reference wave is a plane wave. In other cases, e.g., a spherical wave, Eq. (7) can be employed as long as the structure of the reference wave is known.

2.2 Measurement process

With the propagation approach outlined in section 2.1.2, it is possible to calculate the mutual coherence in the $\delta _{0}$-plane by inserting $z_{2}=-d_{0}$ into Eq. (10). This is the digital holographic analogue to the imaging process provided by the Mirau objective [32] in scanning WLI. Hence, we can record a set of digital holograms with different wavelengths to identify those areas of the object which have the same distance $d_{0}$ to the beam splitter like the reference mirror.

In principle, we could repeat this procedure multiple times while shifting the reference mirror by small amounts $\Delta d$ in-between. This would scan the $\delta _{0}$-plane across the entire object and provide us with enough data to form a 3D representation of the object. Yet, because the spectral modes $\Gamma _{n}$ are stored digitally, it is not necessary to perform any additional measurements or mechanical movements. Instead, we can numerically calculate the coherence function by using the measured $\Gamma _{n}(\vec {x},z_{1})$, and modulating them with the optical path difference of $2\Delta d$ expected from a corresponding mirror shift, which is similar to a simulated temporal scan [33]. For a plane reference wave we therefore define $r_{n}(\vec {x},z_{1}; \Delta d) = r_{n}(\vec {x},z_{1}) \cdot \exp \left (\text {i} k_{n} 2\Delta d \right )$, and with reference to Eq. (5) write

Additionally, because of the shift of the $\delta _{0}$-plane, the propagation distance in Eq. (10) needs to be adjusted, so that $z_{2} = - (d_{0} + \Delta d)$.

Equation 11 is a very important result, because it means we can fully calculate the result of a white light interferometric measurement based on only one set of $N$ recorded holograms. For $N < 10$, this could possibly even be achieved in a single-shot multiplexing arrangement [34]. Because most of the results are numerically calculated, we refer to this process as the virtual measurement cycle. Figure 2 presents a flowchart of the virtual measurement cycle. The result is a stack of propagated mutual coherence functions $M(\vec {x}, \Delta d)$, which is fully compatible with the result of a standard scanning WLI measurement. Hence, any established method in the field can be used to determine the surface profile from it.

 

Fig. 2. Flow chart of the evaluation process (virtual measurement cycle): The process starts with recording of $N$ digital holograms with different wavelengths. To this end, the object is placed in the distance $d_{0}$ below the beam splitter, which equals the distance between reference mirror and beam splitter. From the holograms, the spectral modes $\Gamma _{n}$ are extracted to start the virtual measurement cycle. The cycle consists of adapting the spectral modes $\Gamma _{n}$ to the virtual mirror shift $\Delta d$ using Eq. (11), calculating the mutual coherence in the respective $\delta _{0}$-plane using Eq. (10), storing the result, and determining the next mirror shift according to the next layer position. If all layers have been investigated, the mutual coherence stack $M$ can serve as input to any established method from the field of WLI, to extract the topology.

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2.3 Shape determination

As seen from Fig. 2, the result of the measurement process is the stack of propagated coherence functions $M(\vec {x}, \Delta d)$. In principle, we could follow the coherence scanning scheme and determine the shape of the SUT by simply finding the maximum values of $\vert \Gamma \vert$, so that the profile is determined by

Unfortunately, the maximum value of the coherence function is very susceptible to noise on the measured phase distributions. In our investigations, we observed that even moderate phase noise of $\delta \phi =0.3~$rad can lead to an uncertainty of approx. $\sigma =200~$nm.

This behavior can be well understood in the complex plane: In the noise free case, the maximum of $\vert \Gamma \vert$ coincides with all spectral modes $\Gamma _{n}$ being real valued. The reason is that the path difference between object wave and reference wave is zero, and therefore $\arg \{\Gamma _{n}\}=0$ holds for any $n$. Hence, equivalently to Eq. (12), we could demand

In the noise free case, Eq. (12) and Eq. (13) yield identical results. However, if phase noise is added, the two criteria show completely different behavior. As we expect the $\Gamma _{n}$ to be fully real valued, any phase noise will mostly affect the imaginary part of $\Gamma$. This has a significant effect on the absolute value of $\Gamma$, and therefore Eq. (12. However, the real part $\mathcal {R}\{\Gamma \}$ is almost not affected by phase noise, making Eq. (13 considerably more robust. Interestingly, because it seeks to maximize the real part, so that all phase values of the spectral modes are as close to zero as possible, Eq. (13 yields a similar result as fitting a line through $k$-space, as suggested in Ref.[8] for example. However, we are not only regarding the phase values of the spectral modes but the entire field component. This can be compared to a weighted $k$-space fitting, where the amplitude might be regarded as a measure of confidence. In our work we therefore use Eq. (13, which allows us to determine the profile $h(\vec {x})$ with precision down to the single nanometer range, as we will see below.

2.4 Choice of wavelengths

In the preceding paragraphs, the basic principle of WLI using spectral holography has been outlined. An apparent question is the choice of wavelengths, i.e., the specifics of the sampling scheme in spectral domain. In this paragraph we will therefore discuss some helpful relations which can be derived from basic sampling theory. Let us start with the definition of the discrete spectrum using the power spectral density (PSD)

In our situation, the temporal delay $\tau$ is related to the optical path difference $\delta$ between object wave and reference wave by $\tau = \delta /c$, with $c$ being the speed of light. For the following discussion we will assume that the frequencies $\nu _{n}$ are separated by multiples of a fixed difference $\Delta \nu$. In this case, we can arrange them across a fixed lattice with spacing $\Delta \nu$, and use sampling theory to gain some insights. It is known that a discrete spectrum has a periodic Fourier transform, where the period is given by [36]

Hence, if Eq. (14) is inserted into Eq. (15, the coherence function $\Gamma (\tau )$ can be expected to become periodic and profile measurements will only be unambiguous within one period $\delta _{P}=\tau _{P} \cdot c$. It is important to take this into account when designing a system which is based on a set of discrete, equispaced lines.

A similar relation can be found for the confinement of $\Gamma (\tau )$ along the $\tau$-axis, e.g., the delay $\Delta \tau$ for which the magnitude of $\vert \Gamma (\tau ) \vert$ drops to zero. Ideally, the confinement should correspond to a coherence length $l_{c}=\Delta \tau \cdot c$, which is below the depth-of-focus $z_{D}$ of the imaging system. To estimate the minimum feature size of $\vert \Gamma (\tau ) \vert$, we can make a thought experiment and multiply the discrete spectrum in Eq. (14) with a window function $W(\nu )=\text {rect}(\nu /B)$, where $B$ is the bandwidth of the spectrum. Please note, that the window function does not change the spectrum at all. However, after inserting the windowed spectrum $S_{xx}(\nu ) \cdot W(\nu )$ into Eq. (15), we realize that according to the convolution theorem $\vert \Gamma (\tau ) \vert$ can be thought of being convolved with a sinc-function

Hence, the unambiguity range equals the coherence length times the number of wavelengths, i.e.,

We can fulfill the basic requirement of WLI by setting $l_{c} = z_{D}$, i.e., the coherence length matches the depth of focus. Thus, according to Eq. (19, a spectrum of only $N$ wavelengths is required to perform WLI with an unambiguity range of $N$ times the depth of focus. Let us consider the case of wafer level testing for example, where most of the objects have an extent along the optical axis of less than $20\;\mathrm{\mu}\textrm {m}$. If we create a spectrum with only $7$ discrete lines, we could design a coherence length of $l_{c}= 3\;\mathrm{\mu}\textrm {m}$ and still have an unambiguous result. Looking at the diffraction limited DoF

3. Experimental setup and results

Figure 3(a) shows the experimental setup used for demonstrating the proposed approach. It is based on the sketch introduced in Fig. 1. The reference mirror of the interferometer is tilted to modulate the interference pattern with the spatial carrier frequency required to extract the individual spectral modes $\Gamma _n(\vec x,z_1)$ from the recorded digital holograms. The test object is located at $z_1=81.5$ mm away from the camera domain. The camera is an AVT (Prosilica GT 2750), which provides a periodic sampling grid of $N_{p} \times N_{p} = 2048\times 2048$ pixels with a pitch of $\Delta p=4.54\;\mathrm{\mu}\textrm {m}$ in both directions.

 

Fig. 3. Experimental Flash-Profilometry setup using spectral holography: a) A photograph of the setup shows the beam path. A spherical wave is collimated using a parabolic mirror and then divided into object and reference waves using a $50:50$ beam splitter. The object wave is used to illuminate the surface under test (SUT) and the reference wave illuminates a flat reference mirror. Light reflected from the test object and the reference mirror is recombined and the hologram is recorded using a camera sensor with a pixel pitch of $4.54\;\mathrm{\mu}\textrm {m}$, located at a distance of $81.5$ mm from the test object. b) Photo of the SUT and an example of a digital hologram captured using a wavelength of $\lambda = 632.8$ nm. The insert on the right-hand side shows the spatial carrier frequency applied by tilting the reference mirror to enable the extraction of the complex amplitude using the spatial phase shifting approach.

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A dye laser with a tunable wavelength range from $560$ nm to $615$ nm was used as a variable light source along with a HeNe laser emitting at $632.8$ nm and two solid-state lasers at $532.8$ nm and $488$ nm, respectively, to extent the spectral width. In digital holography, the solid angle which every object point encloses with the camera target defines the numerical aperture and therefore the lateral resolution [11]. In our setup the numerical aperture is approximately the same for each object point and given by $NA \approx (N_{p}/2) \cdot \Delta p/z_{1} = 0.057$. Depending on the wavelength, the lateral resolution is approx. $6~$µm, and according to Eq. (21), the DoF has a range of $150\,$µm to $195\,$µm. The SUT shown in the insert of Fig. 3(a) is a diamond turned reflective aluminum surface with concentric steps provided by the Labor für Mikrozerspanung (LFM) [37]. It has a diameter of $25$ mm and a track width of $0.5$ mm. The SUT has four groups, each consisting of four rings with the same step height difference. Beginning in the center, the first $4$ steps are $5\,$µm, followed by $4$ steps of $10,\, 20$ and $50\,$µm, respectively. Thus, the SUT has a total depth of $340\,$µm. Due to technical limitations of the diamond turning process, the SUT shows fine structures with a height range of $\pm 5$ nm, which have been verified prior to our investigations using a standard white-light interferometer Keyence VKX-3000 with 10x objective having a numerical aperture of $0.3$. By tuning the dye laser from $563$ nm to $604$ nm in steps of $1$ nm, a set of $41$ digital holograms of the test object has been captured, along with three holograms with the additional laser sources at $488$ nm, $532$ nm and $632.8$ nm. As an example, Fig. 3(b) shows the hologram captured at $\lambda = 632.8$ nm.

To reconstruct the shape of the SUT, the following steps, based on the method presented in Sec. 2., have been applied: The first step is to determine the complex valued spectral modes $\Gamma _{n}$ from the captured holograms. This is achieved by applying the spatial carrier frequency method [28,38]. Figure 4(a) shows an example of the amplitude while Fig. 4(b) shows the phase of the complex amplitude obtained from this process after removing the linear phase associated with the carrier frequency. Now, we propagate each of the spectral modes $\Gamma _{n}(\vec {x},z_{1})$ into the object plane to obtain $\Gamma _{n}(\vec {x},z_{2})$ using Eq. (10), so that the central plateau of the SUT is in focus. Across the plateau, we select a small area as a common reference point, where the object height is forced to be zero. This is achieved by subtracting phase offsets, so that the reference area has an average phase value of zero on each of the $\Gamma _{n}$. Please note, that this procedure is required to couple all spectral modes and thereby compensate for unintended movements of the setup during the recording process. An example of the resulting complex amplitude at that plane is shown in Fig. 4(c) and Fig. 4(d).

 

Fig. 4. Intermediate results: a) and b) show amplitude and phase of a spectral mode $\Gamma _{n}$ in the camera plane, as obtained from the recorded hologram in Fig. 3(b) using the spatial carrier method. c) and d) show amplitude and phase of the same $\Gamma _{n}$ in the object plane, as calculated using the propagation operator defined in Eq. (8) and to be inserted into Eq. (10).

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Finally, we perform the virtual measurement cycle, following the scheme introduced in Fig. 2. For this purpose, we calculate the coherence function along the $z$-axis in $20$ nm steps using Eq. (10) and Eq. (11). Across the entire height of $340\;\mathrm{\mu}\textrm {m}$ of the SUT, this means a significant computational effort when using the propagation operator $\mathcal {P}_{\Delta z}$ as defined in Eq. (8). Yet, within the DoF, the light propagates predominantly along the $z$-axis, so that we can approximate

As an example, Fig. 5(a) shows the real part of the mutual coherence function along the $z$-axis for two positions marked in Fig. 5(b). The height difference between the central plateau and the $4^{\text {th}}$ step is correctly determined to be $20.05\;\mathrm{\mu}\textrm {m}$. A height map of the entire surface is shown in Fig. 6(a). We see, that the surface is well reconstructed over the entire axial extent. An analysis of the local surface fluctuations yields $\pm 5$ nm ($1 \sigma$), which is close to the known production related surface deviations.

 

Fig. 5. Examples of the coherence function calculated along the $z$-axis using the virtual measurement cycle introduced in Fig. 2: a) The real part of the coherence function along $z$ is shown for the two positions on the object surface marked by the blue and green dot in b). The shift between the coherence function indicates a height difference between the two points of $20.05\;\mathrm{\mu}\textrm {m}$, which is in very good agreement with the known profile.

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Fig. 6. Measured 3D profiles: a) A step object to demonstrate a large axial range of the method and b) a flat mirror with $\lambda /20$ surface quality to investigate the precision. Both measurements have been achieved by recording less than $50$ holograms with varying wavelengths. The surface of the step object has been accurately determined, showing $4$ concentric steps at a time with heights of $5\;\mathrm{\mu}\textrm {m}$, $10\;\mathrm{\mu}\textrm {m}$, $20\;\mathrm{\mu}\textrm {m}$ and $3$ steps with $50\;\mathrm{\mu}\textrm {m}$. The steep walls connecting the layers have been inserted for visualization purposes. Investigation of the mirror surface yields a precision of $\sigma = \pm 2.5$ nm, as can be seen from the histogram of height values shown in the inset.

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In order to estimate the achievable measurement precision, we performed an additional measurement using a flat mirror with surface finish of $\lambda /20$ as object. For the result shown in Fig. 6(b), $42$ holograms were recorded and evaluated in a wavelength range from $532.8$ nm to $632.8$ nm. The analysis reveals a measurement precision of $\pm 2.5$ nm ($1 \sigma$) across a field of view of $1\,\textrm {cm}^2$. Additionally, we can see spatially low frequent variations in the range of $10$ nm, which most likely result from the surfaces of the optical components in the setup, such as the beam splitter, the reference mirror or the beam collimation in the illumination path. A calibration strategy is needed to compensate for these deviations. Finally, we see a speckle-like spatial noise structure, which results from coherent noise, and diffraction artifacts caused by dust in the beam path.

The results in Fig. 6(a) and Fig. 6(b) demonstrate the potential and the current limitations of white-light interferometry using spectral holography. We required less than $50$ recordings, to accurately measure the SUT with nanometer precision over an axial extent of several hundred microns, showing the compelling dynamic range of the method. The results are comparable to those of white-light interferometry, even though only a fraction of the recordings are required. Additionally, because of the coherent mode coupling described above, the method is robust against vibrations and can be directly integrated into a production environment. In our investigations we used a simple free space propagation approach (Eq. (10)) for the propagation into the object plane. This is appropriate for small numerical apertures. With higher numerical apertures, wavelength dependent spherical aberrations may become an issue because of the beam splitting cube. In this case, the propagation algorithm must incorporate the wavelength dependent refractive index of the cube to compensate for this effect.

A current fundamental limitation is the speckle noise. Unlike in scanning white-light interferometry, the illumination has to be spatially as well as temporary coherent and, as a matter of principle, will create speckle noise on rough surfaces. One solution to this problem is to record multiple holograms under different illumination angles and to average the resulting profiles. This has already been shown to work in multi-$\lambda$ digital holography [39]. However, adding more recordings impairs the advantage of a shorter acquisition time and must be decided based on the application.

4. Conclusion

In this study we have presented Flash-Profilometry, a new coherent profiling method using spectral holography. The idea is to use numerical scanning of the coherence function throughout the surface profile of the object, based on a set of digital holograms recorded using different wavelengths. Our findings show for the first time that it is feasibly to almost completely replicate a scanning WLI measurement using lensless digital holography. Owing to the holographic principle, we avoid problems with depth of field limitations commonly predominant in spectral WLI, while still facilitate measurements with interferometric precision.

To demonstrate its potential towards high precision surface characterization, we have investigated specular surfaces and achieved a precision in the low nanometer range over an axial extent of several hundred microns. The results are comparable to those of scanning WLI. However, in comparison the method provides substantial benefits, such as a reduced number of required recordings. In our investigations we used approximately $50$ recordings, which is one order of magnitude less than required in a typical scanning WLI setting. Additionally, the approach is robust against mechanical distortions. This enables the system to be integrated directly into a production environment. Furthermore, since it is based on digital holography, the method can be implemented using simple Michelson-type configurations and does not need any imaging optics, thereby avoiding dispersion problems while enhancing compactness, weight and flexibility.

In future work we will extend the method to the scheme of optical coherence tomography (OCT) to investigate the feasibility to measure thin-films and transparent media. Additionally, we will add multiple illumination directions to reduce the speckle effect, which currently limits the achievable precision, and potentially the lateral resolution depending on the surface roughness. Finally, we will develop calibration techniques for the presented lensless configuration to improve the accuracy, and develop new system designs for high numerical apertures which are currently impeded by the presence of the beam splitter.

In its current state the measurement system has already a wide range of applications in fields such as optical inspection, e.g., for wafer testing, and material science and is a powerful tool for the precise characterization of surfaces in a production environment.