Surface roughness and surface topography characterisation play critical roles in precision manufacturing [1], defect inspection [2], semiconductor metrology [3], and advanced industrial quality control [4]. Current industrial standards for roughness evaluation are still primarily based on contact stylus profilometry [5–8]. Although contact-based approaches provide highly standardised, traceable and well-established measurement methodologies, the direct mechanical interaction between the stylus tip and the sample surface may introduce scratches or deformation, particularly for soft materials or ultra-precision surfaces. Furthermore, conventional stylus profilometry is inherently line-based and therefore cannot directly deliver full-field surface morphology information; reconstructing a full-field representation generally requires multiple scans, at the cost of increased measurement time and complexity. Non-contact optical metrology therefore provides an alternative approach for quantitative surface characterisation [9].

Existing non-contact surface metrology techniques include white-light interferometry [10–13], confocal microscopy [14–16], digital holographic microscopy (DHM) [17–22], and phase-shifting interferometry (PSI) [23–27]. Among these methods, white-light interferometry achieves high axial resolution through the short coherence length of broadband illumination [28, 29]. By axially scanning the sample or objective lens, the position of maximum interference contrast can be identified and converted into surface height information. Owing to the low coherence of broadband illumination, parasitic interference and speckle-related coherent artefacts are intrinsically reduced compared with narrow-linewidth laser interferometry. However, the extremely short coherence length of broadband illumination imposes stringent requirements on axial scanning precision and mechanical stability, significantly increasing system complexity and cost. In addition, the dependence on mechanical scanning fundamentally limits measurement speed. Long acquisition times increase susceptibility to environmental perturbations such as vibration and airflow, making practical deployment in industrial environments challenging.

Interferometric measurement techniques include DHM and PSI have emerged as powerful approaches for quantitative non-contact full-field surface metrology using coherent laser illumination. These techniques enable direct reconstruction of optical phase and surface topography with high axial sensitivity and without the large-range axial scanning typically required in white-light interferometry [24, 30, 31]. In interferometric measurements, accurate phase retrieval is essential for quantitative interferometric surface reconstruction. Conventional holographic phase retrieval approaches typically rely either on off-axis interferometry [31, 32], where phase information is spatially separated in the Fourier domain, or on multi-step PSI [24]. Although off-axis interferometry simplifies phase extraction, the required spatial carrier frequency limits the usable numerical aperture (NA) and may reduce high-spatial-frequency information due to Fourier filtering [31, 33, 34]. To maximise spatial bandwidth while supporting both large-field imaging (NA = 0.30) and high-NA microscopic imaging (NA = 0.75) configurations, in this work we employ a four-step phase-shifting interferometric architecture. Furthermore, a liquid crystal phase modulator (LCPM) is introduced into the reference arm to generate electrically controlled phase delays negating the need for mechanical motion, enabling stable and full-field phase retrieval.

The performance of coherent interferometric systems is, however, fundamentally limited by the high coherence of narrow-linewidth laser illumination [35, 36]. Scattered optical fields originating from rough surfaces and dust particles as well as stray, parasitic reflections from optical components, may coherently interfere with the reference beam, generating severe speckle noise and larger scale coherent artefacts that degrade fringe visibility, phase stability, and the accuracy of the reconstructed surface morphology. To combat against speckle noise, coherence domain engineering has attracted increasing attention as a promising route towards improving the robustness and stability of coherent imaging and metrology systems. By selectively reducing spatial coherence while preserving sufficient temporal coherence for interference formation, unwanted interference between scattered optical fields can be suppressed without compromising interferometric sensitivity. Conventional approaches for coherence control and speckle reduction have included rotating diffusers [37, 38], vibrating diffusers [39, 40] and fibre shaking systems [41, 42]. However, these methods typically rely on mechanically moving components. In interferometric measurements, even sub-wavelength optical path fluctuations can introduce significant phase instability. Mechanical motion within the illumination system may therefore introduce additional vibration-induced noise and reduce measurement robustness, particularly in high-sensitivity interferometric configurations.

To address the above limitations, in this work, we have deployed a liquid crystal coherence modulator (LCCM), in addition to the LCPM, which is capable of dynamically tailoring the spatial coherence properties of laser illumination without the use of mechanical moving components [43–48]. Under electrical square-wave excitation, these liquid crystal (LC) devices undergo local refractive-index fluctuations resulting in the generation of dynamic speckle illumination (DSI). In previous work, we have quantified the temporal decorrelation time of the generated speckle field to be of the order of milliseconds [49]. During the camera integration time, experiments revealed that dynamically varying speckle fields were temporally averaged, effectively suppressing coherent artefacts and speckle noise at the physical level. This LC-based coherence engineering approach therefore provides a compact, vibration-free, and highly integrable solution for interferometric illumination control.

In this paper. The quantitative reconstruction capability of the proposed LC-enabled interferometric metrology platform is first validated using a calibrated atomic force microscopy (AFM) reference grid representing a structured surface with well-defined topographical features. The reconstructed morphology obtained using the proposed coherence-controlled interferometric system show good agreement with the corresponding AFM measurements, confirming high-resolution surface metrology capability. Following structured-surface validation, measurements are then presented for calibrated stochastic roughness standards. Importantly, the corresponding reconstructed roughness values are found to be consistent both with established industrial roughness standards and conventional contact-based profilometry. In addition to quantitative roughness evaluation, we demonstrate that the dual-LC surface profiler proof-of-concept simultaneously provides both intensity and full-field surface morphology information, enabling quantitative surface characterisation beyond conventional roughness parameters alone. Lastly, results are presented on standards fabricated using different machining processes, which further reveal distinct fabrication-dependent surface morphology signatures.

2.1. Four-phase-shift Interferometry

The surface roughness measurement system was based on a Linnik interferometer [50, 51]. As shown in figure 1(a), the light source was a 532 nm green laser diode with an output power of 3 mW. A static diffuser combined with the LCCM forms a dynamic speckle generation module in the illumination path. The collimated laser beam passed through a diffuser, which transformed it into a near flat-top beam with an increased beam size. The beam was then modulated by the LCCM (figure 1(aii)), significantly reducing the spatial coherence of the incident light field, and lens (L1) collected and re-collimated the modulated beam. A linear polariser (Pol) selected the polarisation direction required by the subsequent LCPM.

Figure 1 (a) Illustration of the layout of the surface roughness measurement system. BS: beam splitter; Pol: linear polariser; L1 and L2: lenses. Insets (i) and (ii) show photographs of the fabricated LCPM and LCCM devices. (i) and (ii) share the same scale bar corresponding to 10 mm. (b) Process flow of the four-phase-shifting method. Controlled phase shifts were introduced using the LCPM and a hologram was captured at each phase step. The wrapped phase map and intensity distribution were then calculated from the recorded holograms. Subsequently, phase unwrapping was performed to reconstruct the final surface phase distribution.

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A 50:50 beam splitter (BS) directed half of the light into the interferometer reference arm. A LCPM (figure 1(ai)) in the reference arm introduced a controllable phase delay without mechanically changing the optical path length. The reference arm employed a 10× objective lens (NA = 0.30), while the sample arm supported interchangeable objective lenses with different NA, enabling scalable surface metrology across multiple imaging conditions and fields of view. A mirror placed in the reference arm provided a reference corresponding to an ideal flat surface. The light reflected from the reference arm interfered with the light reflected from the sample arm, forming a hologram. The interference signal was imaged through a tube lens (L2, f = 200 mm), and the resulting hologram was recorded by a CMOS camera. Additional details of the experimental configuration are provided in the Methods.

Figure 1(b) illustrates the flowchart for calculating the intensity map and the phase map. Quantitative surface reconstruction was performed using a four-step phase-shifting method, in which four interferograms with controlled phase delays of 0, π/2, π, and 3π/2 rad were sequentially acquired using the LCPM. The wrapped phase distribution was reconstructed from the interferometric intensity modulation using a standard four-step PSI algorithm, followed by phase unwrapping to recover the continuous phase. The phase information was subsequently converted into quantitative surface height measurements. Further details of the reconstruction procedure are provided in supplementary information section 1.

2.2. LC-based phase shifting

Reliable phase retrieval in PSI critically depends on the precise generation of stable and repeatable phase delays. Conventional approaches commonly rely on piezoelectric transducer (PZT)-driven optical path modulation [52–54] or mechanically rotated phase retardation optics [55, 56]. While PZT-based methods provide high phase precision, they require mechanically actuated interferometric components and high-voltage driving electronics, which may introduce vibration-induced phase. Mechanically rotated waveplate systems are typically limited in modulation speed and integration flexibility.

Here, electrically controlled phase shifting was implemented using a LCPM, enabling compact, low-voltage, and mechanically stable phase modulation without physical optical path displacement [57–64]. Details of the LCPM fabrication are provided in Methods. The LCPM provided accurate and repeatable phase retardation with millisecond-scale response times, supporting stable and rapid full-field interferometric phase reconstruction (supplementary information section 6). Predictable phase retardation was experimentally observed over the temperature range of 20 °C–50 °C, demonstrating the broad operating temperature range of the LCPM (supplementary information section 8).

The phase-voltage response of the LCPM was characterised using the crossed-polariser calibration system described in Methods and supplementary information section 4. In this configuration, electrically induced phase retardation was converted into measurable intensity modulation and recorded using a photodetector. Figure 2(a) shows the measured normalised intensity response as a function of the applied square-wave driving voltage. The calibration results indicate that the LCPM provided a phase modulation range exceeding 4π rad over a driving range from 0.05–10 Vrms. To minimise temporal overhead during four-step phase-shifting acquisition, voltage operating points which are over 2 Vrms were preferentially selected to exploit the faster LC response dynamics at elevated driving fields. Figure 2(b) presents the corresponding phase retardation extracted from the calibrated intensity response over the 2–10 Vrms operating range.

Figure 2 Calibration of the LCPM. (a) Measured normalised intensity as a function of the applied driving voltage of the LCPM. Details of the calibration process are provided in supplementary information section 4. The LC device was driven using a 1 kHz square-wave signal with a 50% duty cycle. (b) Enlarged view of the dashed region in (a), showing the corresponding phase delay derived from the measured intensity response. Four phase-delay points were manually selected for the subsequent four-phase-shifting measurements. One representative set of selected phase points is indicated by the four red markers with the corresponding voltage. (c) and (d) The demonstration sample was an aged silver-coated mirror containing surface contamination and local coating defects. (c) Vertically stacked interferograms of the same sample region acquired under the four selected phase-shifting states. (d) Surface topography reconstructed from the four-step phase-shifting interferometric measurement.

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Because the LCPM was implemented in a double-pass configuration between the objective lens and the BS in the reference arm, the effective interferometric phase retardation was twice the single-pass phase retardation measured in the crossed-polariser calibration system. Based on the calibrated response, four phase states corresponding to 0, π/4, π/2, and 3π/4 rad were selected at driving voltages of 10, 4.85, 3.23, and 2.57 Vrms, respectively. To achieve these phase delays, the response time of the LCPM was within 55 ms. The temporal response characteristics of these operating points are presented in supplementary information section 6.

As shown in figure 2(c), interferometric images acquired under the four phase-shifting states were processed using the reconstruction workflow described in supplementary information section 1 to obtain the quantitative surface topography information. In this example, the demonstration sample consisted of an aged silver-coated mirror region containing surface contamination and local coating bubble defects. For visualisation, a 170 μm × 170 μm region was extracted from the full 600 μm × 800 μm reconstructed field of view (FoV). The reconstructed topography shown in figure 2(d) contains both genuine mirror-surface features and coherence-induced artefacts. The broad elevated structures near the centre of the FoV correspond to contamination and coating defects on the aged mirror surface. In contrast, the quasi-periodic fringe-like background structures and numerous sharp isolated peaks are not associated with the actual mirror morphology but arise from parasitic interference and coherence-induced phase fluctuations. As these artefacts originate from the high spatial coherence of the illumination rather than the sample itself, they fundamentally limit the fidelity of interferometric surface reconstruction. These observations further highlight the importance of introducing the LCCM to generate DSI to suppress coherence-induced artefacts in full-field interferometric surface metrology.

2.3. LC-based coherence control

In our previous work, we introduced a LCCM for dynamic spatial coherence control of coherent light fields [43–48, 65]. Details of the LCCM are provided in Methods. Under square-wave electrical excitation, dynamic phase fluctuations within the LC layer continuously scramble the optical wavefront, producing DSI with reduced spatial coherence. The associated DSI evolves on sub-millisecond timescales, enabling temporal averaging of speckle fluctuations during detector integration and thereby suppressing coherent artefacts and speckle-induced noise. A simplified analysis of the relationship between speckle suppression, the decorrelation time, and the camera integration time is provided in the supplementary information section 2. The LCCM has previously been demonstrated in laser projection [45, 46, 48], inline DHM [66], and random speckle illumination microscopy [49], highlighting its potential as a versatile coherence-engineering platform. As previously reported, the LCCM was shown to maintain effective speckle suppression from room temperature to 50 °C, supporting its practical operational robustness [46].

For interferometric measurements, sufficient temporal coherence is required to convert optical path differences into measurable phase-dependent intensity modulation. However, implementing coherence control while preserving interferometric phase stability remains challenging. The LCCM addresses this challenge by providing dynamic coherence modulation without mechanically moving components.

Measurements were compared between direct coherent laser illumination and illumination dynamically controlled using the LCCM operating under optimised conditions. A turning roughness standard was selected as the measurement target. For the direct-laser illumination measurements, the entire DSI generation module, including both the diffuser and the LCCM, was removed to avoid additional speckle noise introduced by the diffuser or by the non-operated LCCM. Figures 3(a) and (c) show the reconstructed intensity images and morphology acquired without the LCCM and engineered diffuser, corresponding to direct laser illumination. Due to the high spatial coherence of the laser source, parasitic interference generated by multiple parallel optical interfaces, including the BS and CMOS sensor cover glass, introduced strong coherent artefacts into the interferometric measurement. Furthermore, scattering from dust contamination, optical surface imperfections, and the rough sample surface itself generated significant speckle-induced phase and intensity noise.

Figure 3 Performance comparison of the LCCM in interferometric surface measurement. A turning roughness specimen from the calibrated surface roughness standards was selected as the test target. For the measurements shown in (a), (c) and (e), the LCCM and engineered diffuser were removed from the optical path, corresponding to direct laser illumination. Measurements shown in (b), (d) and (f) were acquired with the engineered diffuser and LCCM operating under optimised conditions. (a) Intensity map acquired without LCCM. Optical imperfections and coherent noise introduce strong intensity fluctuations that obscure surface details. (b) Intensity map acquired with the LCCM enabled. The suppression of coherent noise significantly improves image uniformity and reveals fine surface features with enhanced clarity. (c) Reconstructed surface morphology obtained using direct coherent laser illumination. Although portions of the surface profile remain observable, strong coherent artefacts and speckle noise significantly degrade the phase reconstruction quality. (d) Surface morphology reconstructed with LCCM. Speckle noise and coherent artefacts are effectively suppressed, resulting in a substantially improved height map across the full FoV. (e) Enlarged view of the dashed region in (c), showing localised reconstruction artefacts and coherence-induced distortions. (f) Enlarged view of the corresponding region in (d), demonstrating improved reconstruction fidelity and suppression of coherence-induced artefacts achieved using the LCCM-generated DSI. All scale bars correspond to 200 μm.

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Consequently, the reconstructed morphology shown in figure 3(c) exhibited severe degradation in the lower region of the FoV, where coherent artefacts overwhelmed the true surface height information. The enlarged reconstruction shown in figure 3(e), corresponding to the dashed region highlighted in figure 3(c), further illustrates the detrimental impact of coherence-induced artefacts on surface reconstruction. Local phase distortions generated by parasitic interference obscure the underlying surface morphology, preventing reliable interpretation of the true topographical features. The degradation is even more pronounced in the intensity image shown in figure 3(a), where strong speckle fluctuations obscure nearly all fine surface features.

With the LCCM enabled, the dynamically varying speckle illumination introduced time-dependent random phase modulation into the incident optical field. Under reduced spatial coherence conditions, high-visibility interference was preserved only between mutually coherent optical fields originating from corresponding regions of the interferometer arms. In contrast, parasitic reflections and scattering signals originating from other optical surfaces or spatially separated wavefront components exhibited significantly reduced mutual coherence and therefore contributed only weakly to the recorded interference signal [36]. During the detector integration time, these dynamically fluctuating interference contributions were temporally averaged, leading to effective suppression of coherent artefacts and speckle noise.

As shown in figure 3(d), under the LCCM-generated DSI, parasitic interference and speckle-induced phase noise were substantially suppressed, enabling clear observation of surface morphology across the entire FoV. The corresponding enlarged region shown in figure 3(f) demonstrates the effect of the LCCM. Following suppression of coherence-induced fluctuations and parasitic interference, the reconstructed morphology exhibited substantially improved local fidelity. Surface features that were previously obscured became clearly distinguishable, highlighting the benefit of the LCCM-generated DSI for quantitative interferometric surface reconstruction.

Similarly, the intensity image shown in figure 3(b) exhibits significantly improved image quality compared with direct laser illumination. Even in the presence of surface scratches, defects, and other scattering features, clear intensity contrast and fine surface details remain observable. Under the present 100 ms exposure condition, the LCCM-generated DSI, operating under a 1 kHz square-wave driving signal at 200 Vrms with the duty cycle set to 50%, achieved stable suppression of coherent artefacts without introducing measurable degradation in either the reconstructed morphology or intensity imaging performance. Reconstruction results obtained under other LCCM operating conditions are provided in supplementary information section 3.

2.4. Quantitative surface metrology

Before performing quantitative surface measurements using the dual-LC interferometric surface profiler, background calibration of the interferometric system was required to eliminate residual system-induced phase distortions and ensure accurate surface topography reconstruction. To obtain the system background reference, a λ/10 optical flat mirror (specified at 633 nm) was fixed at the sample position. The corresponding phase and intensity distributions were recorded and used as calibration references during surface reconstruction to compensate for residual system curvature and static interferometric background artefacts. Additional details of the background correction procedure are provided in supplementary information section 9. For each objective lens configuration used in the sample arm, the background calibration only needed to be performed once.

Surface topography measurements fit into two classes: structured surfaces and stochastic roughness surfaces. To directly validate the reconstruction accuracy measurements were performed on an AFM calibrated grids sample representing a structured surface with well-defined topographical features. The reconstructed morphology obtained using the dual-LC interferometric surface profiler was compared with corresponding AFM measurements, serving as a ground-truth reference for quantitative validation.

For a direct comparison, a region of 70 μm × 70 μm was extracted from the interferometric measurement results to match the measurement area of the AFM scan. Figures 4(a) and (b) show the reconstructed surface morphologies obtained by the AFM and the dual-LC interferometric surface profiler, respectively. Cross-sectional profiles along the white dashed lines in the corresponding images were extracted and are shown in figures 4(e) and (f). Comparing with the AFM results, the interferometric measurement is capable of accurately resolving the depth information of the grid structure, demonstrating the accuracy of the proposed system for surface morphology characterisation.

Figure 4 Comparison of surface morphology measurements of an AFM calibration grid: (a) AFM scanning result; (b) reconstructed surface morphology obtained using the dual-LC interferometric surface profiler over a 70 μm × 70 μm region; and (c) the complete 150 μm × 150 μm FoV reconstructed from a single acquisition using the dual-LC interferometric surface profiler. The white dashed box in (c) indicates the region corresponding to the reconstruction shown in (b). (a)–(c) share the same height colour scale. (d) cross-sectional profile extracted along the dashed line in (a); and (e) is corresponding profile extracted from (b).

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In experiments, the AFM required several minutes to complete the scan of the selected region, with 256 × 256 pixels. In contrast, as shown in figure 4(c), the interferometric surface profiler acquired a 150 μm × 150 μm area within 1 s, with 1460 × 1460 pixels. Furthermore, with optimised post-processing algorithms, the frame rate of three-dimensional surface reconstruction can be further improved. To quantitatively compare the reconstructed topographies obtained by the proposed interferometric system and AFM, the depths of individual calibration-grid features were statistically analysed. For the interferometric measurement, all 300 complete grid structures within the reconstructed FoV were included in the analysis, resulting in an average depth of 110 nm with a standard deviation of 1 nm. For the AFM reference measurement, the smaller scan area limited the analysis to 30 complete grid structures, yielding an average depth of 103 nm with a standard deviation of 3 nm. Here, the reported standard deviations represent the variation of individual grid depths within the analysed regions rather than the uncertainty of the measurement system itself. Despite the substantially different measurement areas, the average depths obtained by the two techniques showed good agreement, supporting the quantitative reconstruction capability of the proposed coherence-controlled interferometric metrology platform.

After validating the quantitative reconstruction capability on structured calibration surfaces, measurements were further performed on calibrated stochastic roughness standards specimens. These calibrated roughness standards were manufactured in accordance with ANSI B46.1–1985 and consist of electroformed nickel specimens representing six common machining processes, including Flat Lapping, Reaming, Grinding, Horizontal Milling, Vertical Milling, and Turning. Further details are provided in the Methods. The Turning group of the standard sample set was first selected, and samples with nominal roughness values of 0.406 μm, 0.813 μm, and 1.601 μm were measured. The measurement results are presented in figure 5. Figures 5(a)–(c) show the three-dimensional morphology maps of different areas, while figures 5(i)–(iii) display the corresponding central profiles along the white dashed lines indicated in figures 5(a)–(c). The results clearly demonstrate the increasing surface roughness of the standard samples.

Figure 5 Surface morphology measurement results of the roughness standard samples (Turning group). (a)–(c) show the measured surface morphologies of standard samples with nominal roughness Ra = 0.406, 0.813, and 1.601 μm, respectively. (i)–(iii) are the profiles extracted along the positions indicated by the white dashed lines in (a)–(c).

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For quantitative analysis of surface roughness, the horizontal centreline perpendicular to the machining texture was extracted from each morphology map. This approach is consistent with the methodology used in conventional contact-based profilometry. The arithmetic mean roughness Ra was calculated using the following expression:

where N is the number of sampling points and is the mean value of the surface height. For each reconstructed region, roughness values were calculated from individual line profiles across the FoV. The reported uncertainties represent the standard deviations of the resulting roughness distributions and therefore quantify the spatial variation of roughness within the measured area.

Using the dual-LC interferometric profiler, the quantitative roughness measurements obtained for all calibrated reference specimens are summarised in table 1. The roughness of the measured region shown in figures 5(a) and (i) was found to be Ra = 0.410 ± 0.015 μm. This results agrees well with the corresponding calibrated reference specimen, which is quoted as having a nominal roughness value of Ra = 0.406 μm (16 micro-inches (µin)) with a certified tolerance range of 0.366 μm ⩽ Ra ⩽ 0.447 μm. Likewise, the reconstructed roughness of Ra = 0.771 ± 0.048 μm extracted from figures 5(b) and (ii) compares well with the corresponding calibrated roughness standard that is quoted to have a nominal roughness value of Ra = 0.813 μm (32 µin), with a certified tolerance range of 0.732 μm ⩽ Ra ⩽ 0.894 μm. Lastly, the reconstructed roughness extracted from figures 5(c) and (iii) yields a value of Ra = 1.601 ± 0.095 μm, which is in good agreement with the corresponding calibrated roughness standard of Ra = 1.600 μm (63 µin), with a certified tolerance range of 1.440 μm ⩽ Ra ⩽ 1.760 μm. All reconstructed roughness values were therefore found to be consistent with the certified tolerance intervals of the corresponding calibration specimens while simultaneously providing full-field surface morphology information. These results highlight the capability of the dual-LC interferometric surface profiler for quantitative non-contact roughness characterisation and full-field surface metrology.

Table 1. Quantitative comparison between the reconstructed surface roughness values and the calibrated reference standards.

Group and nominal Ra (μm)Certified tolerance (μm)Measured Ra (μm)TurningRa = 0.4060.336–0.4470.410 ± 0.016TurningRa = 0.8130.732–0.8490.770 ± 0.048TurningRa = 1.6011.440–1.7601.619 ± 0.099Flat lappingRa = 0.0510.046–0.0560.053 ± 0.001GrindingRa = 0.0510.046–0.0560.051 ± 0.001

To further evaluate the surface metrology capability of the proposed interferometric system, measurements were extended to the lowest-roughness calibrated specimens. In this case, the Flat Lapping and Grinding reference specimens are specified as possessing nominal roughness values of Ra = 0.051 μm (2 µin), with certified tolerance intervals of 0.046 μm ⩽ Ra ⩽ 0.056 μm. In order to improve sensitivity to the fine surface structures, the sample-arm imaging optics were modified to include a 40× objective lens (NA = 0.75). The resulting reconstructed surface morphologies are shown in figures 6(a) and (b), while the corresponding extracted line profiles are presented in figures 6(i) and (ii). Here, the area-averaged reconstructed roughness values were measured to be Ra = 0.053 ± 0.001 μm and Ra = 0.051 ± 0.001 μm, respectively, in excellent agreement with the calibrated nominal roughness values of the reference standards. When roughness was evaluated independently for each horizontal profile within the reconstructed regions, the measured roughness values ranged from 0.050–0.056 μm for the Flat Lapping specimen and from 0.049–0.053 μm for the Grinding specimen. All reconstructed roughness values (as shown in table 1) were therefore found to fall within the certified tolerance intervals of the corresponding calibration standards. These results demonstrate the extended capability of the dual-LC interferometric surface profiler in obtaining quantitative non-contact metrology of low-roughness surfaces and sub-100 nm surface variations.

Figure 6 Surface topography measurements acquired using a 40× objective lens (NA = 0.75). (a) and (b) show the measured surface morphologies of Flat lapping and Grinding groups from the calibrated standards set with nominal Ra = 0.051 μm. Corresponding extracted line profiles are shown in (i) and (ii), respectively. The results demonstrate that the system can resolve surface morphologies over a wide roughness range while maintaining full-field measurement capability and high axial resolution.

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We have further evaluated different groups of standard surface roughness specimens. As shown in figure 7, samples corresponding to reaming, vertical milling, and turning processes with a nominal surface roughness of 0.406 μm were selected. In figure 7(a), the reaming sample exhibits a characteristic concave profile while in figure 7(b) the reconstructed surface morphology reveals parallel groove features, which are consistent with the characteristics of the vertical milling process. Lastly, figure 7(c) shows a distinct convex curvature in the reconstructed surface morphology consistent with the turning process. Collectively, these results demonstrate that the proposed technique can provide not only quantitative surface roughness information but also comprehensive surface morphology simultaneously. The proof-of-concept dual LC interferometric surface profiler not only enables identification of the underlying fabrication process during roughness measurement but also enables the extension to high-precision surface morphology characterisation, functioning effectively as a surface profiler.

Figure 7 Surface morphology reconstruction results for standard roughness samples formed with different fabrication processes: (a) reaming, showing a characteristic concave profile; (b) vertical milling, exhibiting parallel groove structures consistent with the machining direction; and (c) turning, presenting a distinct convex curvature. The corresponding optical images are shown below each 3D surface profile reconstruction. The results demonstrate that the proposed method can simultaneously capture both full-field surface morphology and distinguish fabrication-induced features. Scale bars om the optical images correspond to a length scale of 5 mm.

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Previous work has shown the performance and lifetime advantages of incorporating zwitterion dopants into the LC mixture to help promote the onset of electrohydrodynamic instabilities [46]. Here, an LC mixture doped with a small concentration (<1 wt.%) of the zwitterionic Riechardt’s dye was filled into commercially available glass cells (INSTEC S100A200uT180) with a nominal cell gap of 20 µm. Transparent indium–tin–oxide electrodes defined a 10 mm × 10 mm active modulation region, while the inner substrate surfaces were coated with a homeotropic alignment layer (DPI-V011). The LC mixture was introduced into the glass cells by capillary filling above the clearing temperature (LC to isotropic liquid phase transition temperature). Dynamic coherence modulation was achieved by applying amplified square-wave electrical signals to the LCCM electrodes. The driving waveform was generated using a waveform generator (Tektronix AFG3022) and amplified using a 20× voltage amplifier (FLC Electronics A400X).

3.2. Fabrication of LCPM

The LCPM was implemented using a LC glass cell filled with the nematic LC mixture, E7 (Synthon Chemicals Ltd.). The LC material was capillary-filled into the glass cell on a heated stage maintained at 80 °C and subsequently allowed to stabilise after filling. The nominal air gap of the glass cell was 5 µm and the effective area of the cell was 20 mm × 20 mm, providing a uniform relative phase retardation across the active region. A detailed quantitative characterisation of the uniformity is provided in the supporting section 7. Electrically controlled phase modulation was achieved by applying square-wave driving signals generated using a waveform generator (Tektronix AFG3022). Further details of the operating principle of the LCPM are provided in supplementary information section 5.

3.3. Experimental configuration and samples

A 532 nm laser diode (Thorlabs CPS532) was used as the coherent illumination source. The laser beam was expanded and spatially homogenised into a flat-top profile using an engineered diffuser (Thorlabs ED1-S20-MD) prior to illuminating the LCCM. The interferometric system was configured using a fixed Olympus UPlanFL N 10× objective lens (NA = 0.30) in the reference arm, while interchangeable objective lenses were implemented in the sample arm to support different imaging