1. Introduction

In high-precision manufacturing, the workpiece often has to be cleaned from machining fluids prior to optical inspection of its topography. This is mainly due to the fact, that most optical methods are faced with severe problems by either the non-stationarity of a fluid or the possibly unknown refractive index of the layer above the specimen. Therefore, the refractive index has to be measured, since it distorts the measurement results, even if only the topography is of interest. From a metrological point of view, this is a similar situation to the measurement of e.g. thin material slabs or surfaces protected by coatings or varnish. The problem of non-stationary layers can be overcome using single-shot techniques like chromatic confocal microscopy (CCM) [1–4] or spectral interferometry (SI) [5–8]. But these approaches require prior knowledge of the refractive index (with exception of [8], which requires transparent objects). This is also true for classic topography measurement systems like scanning confocal microscopes [9, 10] or white light interferometers (WLI) [11–14]. The problem of missing prior knowledge of the layer’s material was tackled by different approaches: elaborate signal modelling, systems limited to transparent specimens, schemes joining two sensor types, featuring multiple scans (axial or spectral) or even multiple light sources, depending on whether or not dispersion is neglectable [15–19]. Different adaptions of the WLI technique seem to be the most advanced solutions to the problems stated above. There, forward signal modelling or pupil monitoring are used to calculate thickness and refractive index (medium layer thickness) or even ellipsometric parameters (thin layers) [14, 20–23]. However, to the best of our knowledge, for all systems mentioned, prior knowledge of the refractive index of the semitransparent layer or at least some sort of scanning is needed. Therefore, they cover many interesting situations but cannot provide single-shot measurements of all layers, prohibiting applications under changing conditions like strong vibrations or fluid layers.

To solve these problems, we propose a new hybrid principle combining chromatic confocal microscopy and spectral interferometry, which we call “Chromatic Confocal Coherence Tomography (CCCT).” It is a single-shot scheme capable of measuring refractive index, layer thickness and topography of the different surfaces simultaneously. With CCCT, we aim for in-line topography measurement even in presence of not exactly known fluid layers, thickness measurement of varnish layers carrying unknown refractive index or precise single-shot measurement of thin materials.

2. Basic Idea

Refractive media affect the measured thickness in different ways when comparing confocal to interferometric techniques: Interferometry measures an optical path length d_int, which is given by a geometric length d multiplied by refractive index n:

Confocal schemes, on the other hand, underestimate the geometric length by the refractive index, as depicted in Fig. 1: Imagine a specimen consisting of two surfaces and a medium of refractive index n₂ in between, which is higher than the refractive index n₁ (typically air) above the upper surface. Light focussed on the bottom surface gets refracted at the upper surface, reducing the incident angle at the lower surface. Therefore, the light travels a longer path as it would have in air. But the system was calibrated in air (n₁) and therefore assumes the lower surface at a higher position, as depicted in checkered green. Using the numerical aperture of the objective lens NA = n₁ · sin(α), Snell’s law (n₁ · sin(α) = n₂ · sin(β)), and trigonometric considerations (h = tan(α) · d_conf = tan(β) · d), the confocally measured layer thickness d_conf is given by

The combination of Eqs. (1) and (2) yields a polynomial containing the combined measurement result d_comb in the power of 4 and 2, whose positive real-valued solution is given by (assuming n₁ = 1):

Obviously, the NA of the used system has to be known to calculate d_comb in addition to the measured values of d_conf and d_int. Hereby imposed restrictions are touched in section 7. The material’s refractive index n₂ can now be calculated from Eqs. (1) or (2).

 

Fig. 1 A specimen consisting of two surfaces with refractive index n₂ in between. Due to refraction, confocal measurement schemes underestimate the layer’s thickness.

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This way, by combining confocal and interferometric measurement schemes, layer thickness and refractive index can be measured without the need of prior knowledge of the specimen. Note, that for most interferometric systems, we would have used the group refractive index rather than phase index in Eq. (1). Using a chromatically separated focal range in object space as described in section 3, one gets to use the phase index for both schemes. However, dispersion is still correctly to be dealt with (see also section 7).

3. Experimental Setup

Based on Chromatic Confocal Spectral Interferometry (CCSI) [24–27], CCCT is a hybrid technique, combining chromatic confocal microscopy and an interferometric scheme very similar to fourier-domain OCT. In the lab setup (see Fig. 2), an NIR-SLD of about 50 nm bandwidth (Superlum S840-B-I-20, wavelength λ ≈ 810..860nm) is joined via fibre coupler with a spectrometer (Avantes AvaSpec-3648, resolution δλ ≈ 0.06nm) for detection, while the other arm of the fibre coupler is connected to the linnik-type sensor head. There, the core of the single-mode fibre acts as a confocal filter. After collimation by two achromatic doublets (effective focal length 50 mm), a non-polarising 50:50 beam-splitter cube splits the beam in an achromatic reference arm and the object arm. Here, a refraction compensated Diffractive Optical Element (DOE) generates chromatically separated foci in the measurement volume. Using 20x 0.46 microscope objectives (Olympus LMPlanFl), this enables for about 100 μm of focus separation (i.e. measurement range). The intensity of the reference signal can be adjusted using a neutral density filter in the reference arm, which also acts as a coarse dispersion compensation to adopt for the missing DOE.

 

Fig. 2 Schematic of the CCCT setup: A SLD light source and a spectrometer detector are fibre-coupled to the sensor head, where the single-mode fibre core acts as confocal filter. A refraction compensated DOE introduces a chromatic focal separation in the object arm, while the reference arm is built achromatic.

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The lab demonstrator is built as a point sensor to show a proof of principle and enable the investigation of suitable evaluation methods. However, as with the most single-shot sensor schemes based on spectral acquisition, CCCT can be extended to a line sensor by use of cylindrical lenses and an aerial detector instead of the spectrometer line. Two-dimensional measurement grids may also be possible if aerial spectrometers or hyperspectral cameras are available with sufficient resolution. Despite the slower acquisition rate, even a laterally scanned point sensor has the advantage of its (axial) single-shot capability. This property is of special interest in the case of moving layers, e.g. machining fluids, which would also prohibit simpler 2D designs like a swept-source approach.

4. System parameters

CCCT aims for measurement of or through layers of several microns thickness. A layer can be measured, if reflected (or scattered) intensities of both its surfaces lie in the dynamic range of the spectrometer. Also, a minimal layer thickness in terms of the confocal measurement has to be met, as the confocal peaks of both surfaces have to be distinguishable. The maximal measurable thickness is limited by the spectral separation or by the frequency sampling on the spectrometer (in the case of very high spectral separation or very low NA). While the lateral resolution is determined only by the used objective, the measurement’s axial resolution will be limited by the resolution of the different information channels (confocal and interferometric ones). Here, “positional resolution” relates to the axial position of a single surface and a “Rayleigh type” of resolution is discussed below as a minimal measurable layer thickness. In confocal regime, the Centre of Gravity (COG) of the peaks is calculated, yielding a positional resolution of about 1/50 of their FWHM, while interferometric evaluation has shown a positional resolution of below 10 nm in CCSI [26, 27]. To achieve such a resolution, a lock-in like phasing evaluation is needed. For now, a coarser frequency evaluation is used in CCCT, whose resolution is similar to the confocal one (20× 0.46 objective).

In order to detect a surface in the measurement volume, an evaluation of appropriate test signals showed that a reflected or scattered intensity of at least 0.2% is required to get a sufficient signal to noise ratio. For a rough estimation of the applicable parameters, the reflectivity R due to changes in refractive index (n₁ to n₂) is given by Fresnel’s formula. We consider the simplified situation of normal incidence as a worst case scenario, also valid for small NAs:

As shown in Fig. 3, this imposes no problem for most material’s surfaces against air, but stacks of layers can not contain too similar materials. On the other hand, for applications listed in section 1, often one of the surfaces provides a much higher reflected intensity than the others. In this case, the range of allowed materials is limited by the dynamic range of the spectrometer. From CCSI measurements it was determined that a reflectivity range of about 4% to 90% is covered by a single shot in one suited configuration. A higher spread in reflectivity would either lead to saturated spectrometer pixels at the higher peak, or non-evaluable signal levels of the smaller peak, prohibiting single-shot acquisition.

 

Fig. 3 Reflectivity at interface of two materials depending on refractive index n₁ and change in refractive index Δn. Values below 0.2% are not considered measurable.

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The measurement range of the system is limited by the chromatic separation in the object space. For the exemplary 20× 0.46 objective, Δz_CCM = 100μm is reached for a single surface against air. The actual measurement range of CCCT measurements is reduced by the layer (stack) itself, as all surfaces have to fit in one spectrometer frame simultaneously. Hence, the usable range Δz_CCCT can be estimated given some prior knowledge of the specimen’s layers (thickness d_i, refractive index n_i) as (disregarding the last term of Eq. (2)):

For other objectives with longer focal lengths, the measurement range can become limited by the interferometric channel. Theoretically, the used combination of spectrometer and light source provides a maximal measurement range given by the coherence length, which is about Δz_coherent = 5.2mm. Due to practical considerations, the feasible measurement range is much lower. We are limited to spectral interference frequencies, which provide enough periods for stable analysis under their respective confocal envelope (achieved by an offset OPD), but are low enough to be sampled sufficiently. Even using conservatively chosen measurement and evaluation parameters suitable for a robust measurement of almost every possible specimen, this results in a value of Δz_SI ≈ 800μm. Obviously, this value is not a geometric measurement range, but the maximal allowed OPD between uppermost and the lowermost surface of the sample.

The minimal thickness that could be measured most often is also determined by the used objective. For confocal analysis, the upper half of each peak is evaluated (see section 5), so each pair of peaks should be spaced to allow the detected intensity to drop at least to 50% in between (see Fig. 4). However, this only holds for peaks of similar intensity. In most situations, one peak gets more intensity, so we assume a value of two times the FWHM to be more realistic, especially in case of peaks with lower halves broadened by aberrations. For highly unbalanced reflectivities, the minimal confocal thickness of a layer is increased even more, as the high-intensity peak tends to overlap the smaller one due to its high-intensity slopes. In case of the 20x 0.46 objectives, we therefore assume a minimal layer thickness of d_conf/min ≈ 6.6μm.

 

Fig. 4 Minimal detectable confocal distance: Signals from two surfaces and the resulting added signal (dashed). a) Two identical peaks spaced such, that the intensity in between drops to 50%, allowing for COG evaluation of each peak’s upper half. b) Same distance, but one peak provides significantly lower intensity, hence the minimal detectable distance is increased.

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For extremely high NA objectives, the resolution of the interferometric channel might be decisive for the minimal layer thickness. Using the simple frequency analysis described in section 5, pixel pitch calculates to about 3.5 μm after fourier transform. But despite the fact, that these peaks are broadened anyhow, they are evaluated separately, allowing sub-pixel resolution. However, remember that interferometric values overestimate the actual thickness, while confocal results underestimate it.

5. Evaluation process

In this section, as well as in section 6, we will look at a simplified situation, where only two surfaces appear in the measurement volume. All considerations are easily transferred to multilayer samples. There, evaluation can be carried out as described here for each pair of surfaces. This enables a calculation of the surface positions throughout the whole stack of layers. As mentioned above, the resulting signals originate from single measurement spots, but all findings are also valid for measurements from potential line or two-dimensional sensors.

The measurement signal (as seen in Fig. 5) on the spectrometer can mostly be treated as a superposition of two CCSI signals with all wavelengths below the uppermost surface influenced by the refractive material. The signal’s envelope is given by the two non-interfering chromatic confocal peaks, where the lower peak is slightly deformed due to spherical aberrations induced by the semitransparent layer. In the interferometric channel, multiple frequencies are found, given by each surface’s Optical Path Difference (OPD) with respect to the reference mirror and their interaction. Due to the strong confocal separation of different surfaces, the interference signal under each peak is notably dominated by the corresponding frequency and almost unperturbed by other surfaces. So for each wavelet, consisting of its confocal peak and a spectral interference frequency beneath, the confocal peak position and OPD can be evaluated separately.

 

Fig. 5 CCCT signal of a 50 μm fused silica sample after subtraction of reference signal. The difference in frequency under each peak gives d_int, while the peak distance after low-pass filtering is d_conf.

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The chromatic confocal distance d_conf is calculated using the calibrated relation of spectrometer pixels and actual position in the measurement volume applied to the COG of each peak’s upper half after low-pass filtering. To obtain the interferometric distance d_int, both wavelets are evaluated separately: Only parts of the signal below the upper half of the envelope are considered. After Hann-windowing and zero padding, the COG of the upper half of the signal’s Fourier transform is calculated. The difference of the resulting two distinctive OPDs is d_int.

6. First measurements

For the sake of simplicity, the proof of principle measurements presented here are carried out with a point sensor on thin materials providing only two surfaces. By use of the DOE, the axial measurement range is highly extended compared to the initial depth of focus of the used microscope objectives. Hence, objectives of high NA can be used, allowing a lateral resolution suitable for topography measurements. The actual topography of the different surfaces of the specimen may be acquired by lateral scanning of the point sensor or adaption to a line or 2D sensor as stated in section 3.

For first proof of principle measurements, thin slabs of fused silica and diamond were used. This kind of sample provides a single layer of highly constant thickness and similar reflectivity from both surfaces. Also, the refractive index of these materials is very well known. In Fig. 6, the low-pass filtered signal (i.e. confocal information) as well as the separately calculated fourier transforms of each peak from a measurement of a diamond sample (thickness from reference measurements d = 102.9 ± 0.5μm, refractive index over measurement range n = 2.4015..2.4042 [28]) are shown. For each of these peaks, the COG of the upper half is calculated before evaluating their respective distances.

 

Fig. 6 Pre-evaluated signals from 100 μm diamond sample. a) Confocal channel over previously calibrated axial position. Peak distance is d_conf. b) Interferometric channel (OPD). Peak distance gives d_int.

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Unfortunately, the numerical aperture has to be known beforehand in order to use Eq. (3) correctly. The used microscope objectives feature a nominal NA of 0.46. However, due to stray light reduction and optical design parameters of the sensor, the pupil is not illuminated completely, resulting in a lower effective NA. Hence, the actual NA is estimated to be 0.3.

The measured value of d_conf for this diamond sample is 41.1 μm. Using the NA value from above and the correct refractive index of n = 2.403, we get d = 102.8μm (off by 0.1%). The measured OPD d_int = 250.35μm on the other hand corresponds to d = 104.2μm (off by 1%), given the correct refractive index. So both evaluation channels provide quite suitable results for this proof of principle measurements.

However, the very concept of CCCT is to provide a simultaneous measurement of d and n without prior knowledge of the sample. Using Eq. (3), NA = 0.3 as well as d_int and d_conf from above, we get d_comb = 106.4μm (3% off) and n = 2.42 (0.7% off).

7. Discussion

As seen in the previous sections, CCCT provides a simultaneous measurement of layer thickness and refractive index in order to get corrected topography measurements of each surface, even for unknown layer materials. However, there are some issues regarding the experimental setup as well as the evaluation strategy to be dealt with.

Obviously, the actual effective NA of the system has a strong influence on d_comb calculated with Eq. (3). But for now, we had no suitable means of measuring the exact NA of the used configuration. Also, it is an issue of further investigation, which evaluation parameters are best for determining the effective NA for Eqs.(2) and (3). This makes NA rather a fitting parameter of forward modelling planned for the future, than a solid input value. So up to now, an estimated NA is used as described above, providing relatively large uncertainties. Also, NA is only constant over the whole measurement range, if the DOE is located in the rear focal plane of the microscope objective. Due to mechanic restrictions, the DOE can not be placed closer than about 4.7 mm away from its optimal position. The hereby induced change of ΔNA = 0.02 (calculated in ZEMAX) over the whole measurement range vanishes against the absolute uncertainty of the actual NA and is neglected for now, but can be incorporated later.

The second big challenge is to deal with dispersion correctly. Despite the use of the reference arm’s neutral density filter as coarse dispersion balancer, there is still a difference in dispersion of the two interferometer arms. But also if the sensor itself would be perfectly balanced, almost every semitransparent object would introduce additional uncompensated dispersion. For the diamond sample discussed above, the interferometric value d_int varies below 2% when using n_835nm = 2.403, or the group index n_g = 2.448. Which is sufficient for the proof of principle measurements but has to be modelled correctly in the future.

Reflected light from different surfaces of the sample also interferes directly, resulting in additional frequencies in the signal. These frequencies are much lower than the ones corresponding to the OPDs between object surfaces and reference. The envelope of the signal (i.e. confocal channel) tends to be deformed by this interference, depending on the specimen’s position in the measurement volume. Especially as this effect is observed even outside the actual measurement range, it seems to be caused by light propagating unaffected by the DOE. Hence, the deformation of the confocal peaks could be reduced by obscuration of the DOE’s centre part.

Also, for now we used a rather easy but stable frequency analysis in the interferometric regime instead of a more precise phasing analysis as seen in [26, 27]. Thus, both channels provide vaguely the same resolution in case of the 20x 0.46 objectives. In future, a more precise phasing evaluation may provide a better resolution for the interferometric values, which may lessen the sensitivity of d_comb to uncertainties in d_conf and d_int.

Especially the confocal channel is affected by aberrations introduced by the layered specimen itself, resulting in an increased uncertainty. These may be modelled and corrected for. However, the really challenging tasks for future research are to consider the local curvatures of each surface and the resulting effects, as they act as optical elements. The effects range from strong lateral and small axial shifts for tilted plane surfaces to all kinds of complex axial and lateral shifts due to defocus and such. But given the adequate lateral and axial resolution the system provides for each surface, a detailed modelling process of the specimen’s shape seems feasible, giving rise to a thoroughly corrected measurement of the whole stack in a single shot.

8. Conclusion and outlook

Chromatic Confocal Coherence Tomography was proposed as a new single-shot manner of measuring thickness and refractive index of semitransparent materials simultaneously in order to provide a corrected topography of unknown multilayer specimens. Due to a combination of chromatic confocal and interferometric techniques, a high lateral, as well as axial, resolution is achieved while maintaining an extended axial measurement range. The minimal measurable thickness and positional resolution of surfaces are limited by the numerical aperture of the used microscope objective.

First proof of concept measurements of a 100 μm diamond sample showed discrepancies of well in the 3%-range for thickness and refractive index. However, there is still potential to decrease the overall measurement uncertainty in future works: The effective NA of the sensor has to measured/modelled as it influences results directly. Uncompensated dispersion in the interferometer has to be handled in more detail. A more precise phasing evaluation of the interferometric signal may provide a higher resolution, thus a lower sensibility of the combined result to measurement errors in both channels. Finally, in order to get a robust off-the-shelf measurement of higher frequency surfaces, influences from the local curvature of the upper surface on the measurement of lower surfaces in terms of lateral and axial deviations have to be modelled for correction.