1. Introduction

Digital Holographic Microscopy (DHM) is an interferometric measurement technique enabling simultaneous retrieval of amplitude and quantitative phase of the complex optical field reflected from or transmitted through a sample [1]. The quantitative phase information provided by DHM has found numerous uses in the field of life sciences [2–8]. In a reflection geometry, the phase image can be converted into height information. The particularity of DHM compared to other quantitative phase imaging method is the off-axis interference of object and reference beams on the camera. The numerical processing of interference fringes provides single-shot phase and amplitude information, without the need of phase-shifting algorithms. This is particularly useful for measuring the topography of dynamical systems such as micro electro-mechanical devices [9].

Of upmost importance for DHM and other interferometric measurement techniques is the bandwidth of the light source. The bandwidth Δλ of a source is inversely proportional to its coherence length. First demonstrations of DHM were performed with nearly monochromatic laser lines, with the resulting images being polluted by multiple reflections within optical components. The use of broader band sources — featuring shorter coherence length — enabled a strong reduction of the spurious patterns [10]. This reduction occurs thanks to a coherence gating effect, which ultimately limits the height of a structure measurable in a single shot to half the coherence length. Coherence gating with broadband sources is also exploited for extracting depth information — or sectioning — in techniques such as optical coherence tomography [11,12] and white light interferometry [13,14], and has also been evaluated in the context of DHM [15,16]. The drawback of short coherence in off-axis DHM is a reduction of the interference area on the camera, a problem that can be alleviated by an appropriate correction of the reference coherence plane tilt [17].

The other important parameter of the source spectrum is its center wavelength λ. It has been demonstrated that a reduction of speckle noise can be obtained by averaging the information obtained from different wavelengths [18, 19]. With proper phasing, the combination of phase information obtained at several different wavelengths also provides a sectioning ability [20–24]. In transmission geometry, multiple wavelengths can be used to decouple thickness from refractive index in biological cells [25,26], or to provide spatially-resolved spectro-refractometric information [19,27].

In a single-wavelength interferometric reflection measurement, the well known issue of phase ambiguity limits the range of unambiguous step height measurement to λ/2. Numerical algorithms are routinely used to unwrap the phase when measuring the topography of smooth surfaces, but generally fail in the case of high-aspect ratio structures or rough surfaces. A workaround is to lift the phase ambiguity by using two or more wavelengths. Well established in interferometric measurements [28–30], the method has ben applied to DHM to measure structures up to several-micron tall [31–34]. Interestingly, DHM offers the possibility of Fourier domain multiplexing for the single-shot measurement of dual- or triple-wavelength holograms [35–37]. Dual-wavelength holograms can also be acquired in a single shot using a color camera [38].

The generation of multiple wavelengths can be obtained by the simultaneous use of several distinct laser sources [32–36], or sequentially with tunable dye or diode lasers [18,20–22,29]. Alternatively, a single broadband source may be used and filtered at the wavelengths of interest. Broadband sources such as tungsten lamps and LED are commonly available for microscopy. LED-based digital holography has been demonstrated [10, 39, 40]. However, the issue with these sources is their limited spatial coherence, setting high requirements in terms of optical alignment and wavefront matching. These requirements are unpractical especially in the case of off-axis and reflection geometries. Sources with low spatial coherence can still be used in off-axis holography once they have been spatially filtered, as in [10]. However spatial filtering results in low illumination intensity that needs to be compensated for by long exposure time. Sources with low spatial coherence are also known to generate artifacts such as the halo effect in the phase measurement, as demonstrated in the case of diffraction phase microscopy [41]. For a spatially coherent broadband source, one should turn to super-continuum lasers or superluminescent diodes. Spectral filtering of the broadband source can be simply obtained with bandpass filters [40], however without tunability of the bandwidth or wavelength. Multi-wavelength digital holography has been realized using a tunable source based on acousto-optical filtering [19, 23]. However, the use of acousto-optical filtering may reveal itself unpractical in off-axis geometry because of the presence of spectral side-lobes and limited possibilities for the tuning of bandwidth. While advanced methods involving apodization and time-resolved arbitrary waveform generation of the radio-frequency drive provide possibilities to reduce side-lobes and broaden the spectrum [42], the conventional use of acousto-optical filters in the context of off-axis digital holography results in a reduction of the field of view because of the too short coherence length [19]. Rapid tuning of the wavelength for quantitative phase microscopy has been demonstrated using a custom-built source made of a diffraction grating, a galvo-mirror and a pinhole-sized aperture [8, 27]. This scheme offers the possibility to customize the bandwidth by optical design, and may enable real-time bandwidth tunability based on a control of the coupling into the aperture.

In this paper, we use a spatial light modulator (SLM) to filter the spectrum of a supercontinuum laser, for application in DHM. SLMs have already been used in phase imaging techniques such as spatial light interference microscopy [43], diffraction phase microscopy [25,41,44] or other methods [45–47]. In [25], the authors combine the SLM and diffraction grating naturally present in a diffraction phase microscopy setup to achieve spectral filtering of the light transmitted through the sample. The drawback of this method is the reduced dynamic range due to the whole spectrum being transmitted in the interferometer’s object arm, which may translate in increased phase image noise. In our case, the SLM is installed in a ‘pulse-shaper’ configuration, as used in ultrafast optics experiments [48,49], enabling control over the bandwidth and wavelength of the DHM illumination. We exploit the control over the bandwidth to tune the coherence length and adapt for the off-axis interference angle to generate full-field holograms. As an application example of wavelength control, we generate sequences of different illumination wavelengths for an Optical Phase Unwrapping (OPU) algorithm, allowing us to measure step heights up to 50 µm, while maintaining the interferometric precision of DHM.

2. Experimental setup

2.1. Spectral control

The experimental setup is sketched in Fig. 1(a). The broadband source (BBS) is a super-continuum laser (WhiteLase SC-400-6, Fianium), whose spectrum is filtered between 550nm and 700nm using edge pass filters. This 150nm broad spectrum is then modulated with the apparatus shown in the inset of Fig. 1(a). It consists in a transmission phase grating (1.86 µm period, recorded as a volume holographic grating as described in [17]), a plano-convex cylindrical lens (f=80mm, Thorlabs), and a reflective liquid-crystal-on-silicon SLM with 512×512 phase pixels (XY SLM, Meadowlark Optics). This arrangement is known as a ‘pulse-shaper’, originally developed by the ultrafast optics community [48, 49]. In this configuration, the spectrum is dispersed by the grating and mapped by the lens onto the horizontal coordinate of the SLM. Therefore each SLM column can independently modulate one spectral component.

 

Fig. 1 (a) Sketch of the experimental setup: a DHM in reflection geometry (details in Section 2.2). BBS: Broadband source (supercontinuum laser). HWP: Half-wave plate. PBS: Polarizing beam splitter. L₁–L₃ are spherical achromatic doublets. BS: Beam splitter. MO: microscope objective. Inset: Spectral control apparatus: “pulse-shaper” (details in Section 2.1). G: Transmission diffraction grating. CL: cylindrical lens. M: pick-up mirror. SLM: spatial light modulator. (b)–(d) Examples of SLM patterns. The spectral components of the incoming beam are mapped along the horizontal axis of the pattern. The 256 phase levels are encoded in gray scale for the figure. (b) is a simple sawtooth pattern to diffract the reflected beam upward. (c) adds a linear correction to the sawtooth frequency as a function of the horizontal coordinate, so that all spectral components diffract in the same direction. (d) is a combination of (c) with a gaussian amplitude filter to select a gaussian portion of the spectrum in the diffracted beam.

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Typical SLM phase patterns are shown in Figs. 1(b)–1(d). We use sawtooth phase patterns such as the one shown in Fig. 1(b) to diffract upward the spectral components, which then back-propagate through the lens and grating and are reflected on a pick-up mirror for injection into the DHM setup. The use of a sawtooth diffraction pattern enables the simultaneous phase and amplitude modulation of the spectrum, through the phase and amplitude of the sawtooth [48,49]. Although we do not exploit phase modulation in the present paper, we still use this diffraction configuration as it allows us to pick-up the modulated spectrum in a different direction than the light reflected from the SLM coverslip, thus minimizing the amount of unwanted spectral components. Using a simple sawtooth pattern (Fig. 1(b)), the different spectral components diffract on the sawtooth with slightly different angles. To prevent this effect, we introduce a linear correction to the sawtooth period as a function of the horizontal SLM coordinate, such that all spectral components back-propagate in the same direction. Such a pattern is shown in Fig. 1(c). Then we can select the spectral components with an arbitrary shape by modulating the amplitude of this pattern as a function of the horizontal SLM coordinate. For example the SLM pattern for a gaussian filter is shown in Fig. 1(d). In more details, the SLM enables modulation of the phase on 256 levels (shown as gray levels in Figs. 1(b)–1(d)). The phase stroke being wavelength dependant, an optimal calibration of the device should take into account that every SLM pixel column is modulating a different wavelength. However, we have noticed that the diffraction efficiency of a 256-phase level sawtooth is close to maximal for the whole bandwidth used in the experiment, even when using a non-wavelength dependent calibration table (look-up table for 635 nm provided by the manufacturer).

In summary, the SLM pattern can be expressed as a function of vertical (i = 1, … 512) and horizontal (j = 1, … 512) SLM coordinates, with an expression of the form

To calibrate the horizontal axis of the SLM as a spectral axis, we generate gaussian filters at different horizontal positions and measure the resulting spectrum using a spectrometer (0.4 nm resolution). We fit the spectra with gaussians, and then fit the obtained center wavelengths with a quadratic fit to obtain the spectral calibration of the SLM horizontal axis.

Gaussian with different widths can be generated, allowing us to control the bandwidth of the illumination. Examples are shown in Fig. 2(a). In the limit where the gaussian width becomes comparable to the pixel size, the resulting gaussian spectrum has a decreased intensity, as shown with the narrowest spectrum of Fig. 2(a) (FWHM = 0.94nm), which corresponds to a FWHM of ~ 3.3 SLM pixels.

 

Fig. 2 (a) Illumination spectra obtained with gaussian filters of different full width at half maximum (FWHM): Δλ = 21 nm, 4.8nm, and 0.94 nm, at center wavelength λ₀ = 620.2 nm (solid lines). Dashed line: full illumination spectrum as obtained using SLM pattern of Fig. 1(c). (b)–(d) Reconstructed amplitude of Sample 1 obtained with the above-mentioned three different illumination bandwidths. Scale bar: 100 µm. (e) Reconstructed phase using Δλ = 0.94 nm. The phase gray scale ranges from −π (black) to π (white).

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2.2. Digital holographic microscope

The spectrally modulated light source is directed to a digital holographic microscope in a reflection geometry [1], as depicted in Fig. 1(a). In brief, the illumination is split into two arms: one object arm and one reference arm. In the object arm, the light reflected from the object is collected by a microscope objective. An image is formed on the camera using lens L₃ that serves as a tube lens. The reference arm is expanded by the telescope formed by lenses L₁–L₃, and interferes with the object arm on the camera sensor (HXC40, Baumer, of which we use a region of interest of 1024×1024 pixels). All spherical lenses are achromatic doublets. L₁ and L₂ have a focal length of 75 mm, and L₃ of 200 mm. The microscope objective (MO) is an Olympus N-plan 10×, NA = 0.25. The delay between the two arms is controlled by a retroreflector on a delay stage. An angle of ~2.3° between the object and reference arms causes interference fringes to be formed on the camera sensor. Amplitude and phase information can be numerically extracted from the recorded digital hologram [1]. The angle of 2.3° is chosen such that a period of the interference fringes (which are oriented along the diagonal of the sensor) is sampled by $\frac{4}{\sqrt{2}}$ pixels. This sampling allows us to eliminate the DC term from the hologram while maximizing the lateral resolution of the image. In case of significant scattering by the object, the interference angle needs to be increased to properly filter out the DC term [50]. For each acquisition, optical aberrations are numerically corrected using a reference hologram recorded on a flat area nearby the structure of interest [51]. An additional phase tilt correction may be used in cases where the reference area is not parallel to the area of interest [52].

2.3. Test samples

The experimental demonstrations of Section 3 are performed with three different reflective samples.

These samples will be further on referred to as sample 1, 2 and 3, respectively.

3. Results

Our spectral control apparatus enables simultaneous tuning of the bandwidth and center wavelength of the DHM illumination. In this section, we show applications of the control of bandwidth (Section 3.1) and center wavelength (Section 3.2) of the illumination.

3.1. Control of coherence length

The effect of the illumination bandwidth in the DHM can be appreciated in Figs. 2(b)–2(d), which shows reconstructed amplitude images of sample 1 for three different bandwidths: 21 nm, 4.8 nm and 0.94 nm, respectively. The bandwidth Δλ is linked to temporal coherence, and thus to the coherence length l_c. For a gaussian spectrum of center frequency λ₀, we have [53]:

3.2. Multi-wavelength Optical Phase Unwrapping

Control of the wavelength can be used for the sequential generation of different illumination wavelengths. We show below how this can be exploited to extend the unambiguous phase range of a DHM measurement, within the framework of a hierarchical Optical Phase Unwrapping (OPU) algorithm.

3.2.1. OPU : principles

In a single-wavelength interferometric reflection measurement, phase ambiguity exists for measurement of step heights exceeding λ/2. Combining information from two measurements with different wavelengths λ₁ and λ₂, the unambiguous phase range can be extended to half of the synthetic wavelength ${\mathrm{\Lambda }}_{1,2}=\frac{{\lambda }_1{\lambda }_2}{\left|{\lambda }_1-{\lambda }_2\right|}.$ While arbitrarily large synthetic wavelengths can be obtained by choosing close enough λ₁ and λ₂, the noise in the reconstructed topographic profile also scales with the synthetic wavelength. To maintain the high precision of single wavelength digital holography, the synthetic phase map can be used as a guideline for unwrapping the phase maps recorded with λ₁ and λ2 [28,29,32,33,36]. To limit the number of unwrapping errors, we define an “acceptable noise threshold” by satisfying the inequality [50]

The maximal unambiguous range is set to half the largest achievable synthetic wavelength. Two distinct wavelengths need to be separated at least by their linewidth δλ, yielding a synthetic ${\mathrm{\Lambda }}_{max}=\frac{{\lambda }^2}{\delta \lambda }$. The tallest step height that can be unambiguously measured is therefore ultimately limited by the coherence length of the illumination (i.e to l_c/2 = 142 µm at 550 nm, the shortest available wavelength of our experimental configuration). It should be noted that approaching this limit will also decrease the interference contrast, therefore increasing the phase noise of the measurement.

3.2.2. OPU: results

Here we show the experimental implementation, using different wavelengths sequentially generated by the pulse-shaper, of a hierarchical OPU algorithm. Briefly, the main steps are the following (more details can be found in references [32,33,36]):

Using the pulse-shaper, we generate gaussian spectral filters at three different wavelengths λ₁ = 650.3 nm, λ₂ = 559.7 nm, and λ₃ = 575.3 nm, with bandwidth Δλ = 0.94 nm. The spectra are shown in Fig. 3(a). As an example, the phase map ϕ₂ obtained using λ₂ is shown in Fig. 3(b). Line profiles of the height maps h_i=1,2,3 are shown in Fig. 3(c). The line profiles of h_i=1,2,3 coincide for the measurement of the step height of ~130 nm, as expected since it is not exceeding λ_i=1,2,3/2. However, h_i=1,2,3 give different values for the step height of ~4 µm.

 

Fig. 3 (a) Illumination spectra obtained with gaussian filters of different center wavelengths λ₁ = 650.3 nm, λ₂ = 559.7 nm, and λ₃ = 575.3 nm, with bandwidth Δλ = 0.94 nm (solid lines). Dashed line: full illumination spectrum as obtained using SLM pattern of Fig. 1(b). Inset: Zoom on the spectrum of λ₃ (dots) with a gaussian fit (solid line) (b) Phase map ϕ₂ obtained using λ₂ on Sample 1. Scale bar: 100 µm. The blue line shows the position of line profiles displayed in (c). (c) Line profiles of height maps $h_{i=1,2,3}=\frac{{\varphi }_i{\lambda }_i}{4\pi }$ (without unwrapping).

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In order to correctly measure this step, we combine the phase information from the three wavelengths, as illustrated in Fig. 4. The corresponding synthetic wavelengths are Λ_1,2 = 4.02 µm and Λ_2,3 = 20.6 µm. The largest synthetic wavelength was chosen such that it enables unambiguous phase measurement on a step height of more than 10 µm. The smaller synthetic wavelength is chosen such that Equations (4) and (5) are satisfied for σ_ϕ = 5.9°. In Fig. 4(a) we show a line profile of H_1,2, obtained by combining the phase information from measurements with λ₁ and λ₂. The ~4 µm step is still not correctly measured, since it exceeds Λ_1,2/2 = 2.01 µm. In Fig. 4(b) we show a line profile of H_2,3. The ~4 µm step is retrieved, since it does not exceed Λ_2,3/2 = 10.3 µm. However, it can be observed that the noise on H_2,3 is large, which is expected since it is amplified by a factor $\sqrt{2}{\mathrm{\Lambda }}_{2,3}/\lambda ~50$ with respect to the single-wavelength measurement. Nevertheless, it can be used as a guideline to unwrap H_1,2. The unwrapped height profile $H_{1,2}^{\ast }$ is shown in Fig. 4(c). Then $H_{1,2}^{\ast }$ can in turn be used to unwrap the single-wavelength height profiles h_i=1,2,3. The average of the unwrapped height profiles $h_{i=1,2,3}^{\ast }$ is shown in Fig. 4(d). This is the final result of the OPU algorithm, featuring a correct height profile and interferometric precision (further enhanced by the averaging over three different wavelengths [18]). The whole height map is shown in Fig. 4(e).

 

Fig. 4 (a) Line profile of H_1,2 (obtained by combining phase information from measurements with λ₁ and λ₂), at the position shown by the blue line in Fig. 3(b). The height range is limited to Λ_1,2/2 = 2.01 µm. (b) Line profile of H_2,3. The height range is limited to Λ_2,3/2 = 10.3 µm. (c) Line profile of $H_{1,2}^{\ast }$, the height map obtained by unwrapping H_1,2 using H_2,3 as a guideline. (d) Line profile of the average of $h_{i=1,2,3}^{\ast }$, the height maps obtained by unwrapping h_i=1,2,3 using $H_{1,2}^{\ast }$ as a guideline. Inset: close-up view on the lower step. Horizontal subdivisions are 20 µm. Vertical subdivisions are 50 nm. (e) Full image of h_OPU, the average of $h_{i=1,2,3}^{\ast }$. Scale bar: 100 µm.

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As an industrial application example, we present measurements of Sample 2, a semiconductor sample featuring arrays of bumps. We use a similar wavelength sequence as for Sample 1, but add one more wavelength such that Λ_3,4 = 100 µm, enabling thus measurement of structures up to 50 µm tall. The resulting h_OPU is displayed in Fig. 5(a). It shows that the bumps are in average ~16.5 µm tall. A close-up view of one bump is shown in Fig. 5(b). In is interesting to notice that the height is well resolved only at the top of the bump, while its edges show inconsistent values. This is expected as the 0.25 numerical aperture objective can only collect light reflected from surfaces with a slope lesser than 7.2°. Light bouncing from the ~80° steep slopes of the bump edges is therefore not collected. It can be appreciated in the reconstructed amplitude image of Fig. 5(c), which shows that the corresponding area is essentially dark (i.e. where the phase is not well defined). A common practice for phase rendering is to discard phase pixels using a threshold condition based on the amplitude map, as for example in [9]. We apply this method in the line profile shown in Fig. 5(d).

 

Fig. 5 (a) OPU height map h_OPU recorded from Sample 2. The dotted square shows the view area of the close up in (b)–(c). The dashed line is where the line profile of (d) is measured. Scale bar: 10 µm. (b) Close-up view of h_OPU. (c) Reconstructed amplitude map of the same area. (d) Line profile of h_OPU. A threshold based on the amplitude map as been applied to discard points where the phase is undefined.

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As a last example, we present measurements of Sample 3, a calibrated step height of 49.394 ± 0.264 µm. A 3D view of the step, reconstructed from data points, is shown in the inset of Fig. 6(a). For this sample only we use a 2.5× microscope objective (Leica N-plan, NA = 0.07) to increase the field of view (FOV) and depth of field. We have generated a wavelength sequence such that Λ_3,4 = 128.6 µm, and with an acceptable noise threshold of 5.2°. We show h_OPU in Fig. 6(a), and a line profile of it along the blue line in Fig. 6(b). The ~ 50 µm step height is correctly retrieved using our multi-wavelength DHM measurement. The same line profile is plotted in (c) on a close-up scale to reveal details of the top and bottom part of the step. In particular, this measurement shows that the bottom part of this calibrated sample is not flat. However, the whole profile still remains within the specified step height of 49.394 ± 0.264 µm. Let us note that no light was collected by the microscope objective from the very steep edges of the step, which carry random values in the phase image (and thus in the height image of Fig. 6(a)). For clarity, in the line plots of Figs. 6(b)–6(c) we have removed these points by using a threshold condition based on the amplitude image. Figure 6(a) also allows us to illustrate the concept of the acceptable noise threshold. While the central part of the FOV is mostly free of OPU errors, some erroneous pixels appear in the edges of the image. We generally measure a spatial noise standard deviation of σ_ϕ < 3° in the central part of the FOV, but reaching higher values in the edges. This is due to the off-axis configuration, providing lower interference contrast in the corners, and to a non-uniform illumination (lower intensity in the edges). In this case, the noise in the edges of the FOV visibly exceeds the acceptable threshold of 5.2° that we had chosen for this sequence.

 

Fig. 6 (a) OPU height map h_OPU of Sample 3. Scale bar: 20 µm. Inset: 3D view of the step reconstructed from h_OPU. (b) Line profile of h_OPU plotted on the full height range of the data. A threshold based on the amplitude map as been applied to discard points where the phase is undefined. (c) Same data as in (b) but with the vertical scale expanded to see details of the top and bottom parts of the step.

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4. Discussion and conclusion

We have shown in the previous sections that our SLM-based pulse-shaper apparatus enables simultaneous and versatile control over the bandwidth and wavelength of the DHM illumination. These features provide the potential to adapt the light source to various experimental conditions (off-axis interference angle, sensor characteristics), sample characteristics (strength of scattering), and modalities (sectioning, multi-wavelength algorithms). Assessed in the context of DHM, the use of this spectral control technique can also be potentially extended to other interferometric and coherent imaging methods. For example, rapid switching of coherence length may be exploited for the purpose of single-source multi-modal imaging.

As an application example we have shown that sequentially generated gaussian filters at different center wavelengths can be used to extend the phase unambiguous range of DHM within the framework of a hierarchical OPU algorithm. Although not single-shot, the technique may still be faster than other 3D profiling techniques such as white light interferometry or confocal microscopy, as it doesn’t require any mechanical motion. Considering a typical 15 ms exposure time and a 5 ms SLM switching time (achievable if the OverDrive Plus option of the device is enabled), our apparatus can potentially acquire a four-wavelength sequence at a rate of 12.5 Hz. While acousto-optic filtering may provide a faster rate, it would be at the cost of loosing control over the bandwidth and line shape of the spectrum.

The use of broadly spaced different wavelengths induces constraints in the system design in terms of chromatic aberrations, which can limit the performance of the DHM (e.g. lateral resolution, or compatibility with larger magnification microscope objectives). Methods to increase performance of multi-wavelength DHM have been previously published, and are beyond the scope of this paper. For example, it is possible to numerically correct chromatic aberrations by adjusting the holographic reconstruction distance for each wavelength independently [34]. The advantages of tele-centric designs have also been discussed [55], and one may also consider the use of apochromatic optics.

The maximal extent of the wavelength tunability (which for example sets the larger acceptable noise threshold for OPU) depends on the bandwidth of the BBS, and also on the design of the pulse-shaper. For example, a less dispersive grating and/or shorter focal cylindrical lens would provide a larger available bandwidth. However it would also increase the width of the narrowest achievable gaussian filter. The limiting factor is thus the resolution of the SLM. For more flexibility, SLMs with a larger number of pixels may be considered.

The limiting factor of the measurement accuracy of a large step is not directly linked to the pulse-shaper itself, but to the precision of the wavelength measurement device. In our case, the 0.4 nm resolution spectrometer provides a relative uncertainty of ~0.07% on the wavelength, translating into a relative uncertainty of a step height measurement. While small topological variations are still measured with interferometric precision (limited by the camera electronic noise, in our case σ_ϕ ≲ 3° corresponds to 2.5 nm), the height of a larger step can only be determined within ~0.07% (i.e. a 35 nm uncertainty for the ~ 50 µm step measured in this paper).

A practical limit to an out-of the-lab use of our apparatus is set by the robustness of its wavelength calibration. In this free space device, changes in the positioning of the grating, cylindrical lens or SLM, or in the BBS alignment, induce a change of the wavelength calibration. While we observed that the calibration remains stable within a day of operation (within our spectrometer resolution), wavelength stability cannot be ensured on the longer term without regularly re-calibrating the device.