Coherence scanning interferometry (CSI) is used for a wide field of applications in research and industry [1,2]. CSI enables the measurement of rough surfaces through the evaluation of the coherence peak. On (locally) specular surfaces, measurements with interferometric precision can be achieved using phase evaluation [3–5]. Current research topics in CSI are the measurement of steep surfaces and signal modeling beyond the linear regime [6–8]. In CSI, the sample under test (SUT) is scanned relative to the reference mirror. The intensity is captured while scanning with a sampling interval of typically tens of nanometers. In modern CSI systems, a digital camera with a charge coupled device (CCD) or a complementary metal-oxide-semiconductor (CMOS) sensor is used. These systems capture for each of the sampling steps the interference signal over the whole field of view (FOV). The product of the maximum framerate and spatial sampling distance limits the possible scan speed. CSI uses a light source with a large spectral bandwidth and thus short coherence length. Therefore, when using CSI for the measurement of steep surfaces, only a small portion of the FOV carries interference signals, the major part of the captured frame just records the background intensity. This drawback of frame based capturing limits the possible scan speed of the measurement in a very fundamental way.

As a solution to this dilemma we propose event based CSI (eCSI): CSI based on novel event based sensors that have become available just recently [9]. An event based sensor is a sensor inspired by the working principle of the human eye [10–12]. It only records when the change of the illumination of a pixel exceeds a threshold. Therefore, a fully asynchronous pixelwise stream of changes is gathered as the sensor signal. Since the output of the camera is only the activated pixels, the sensor signal is sparse, reducing the data redundancy and leading to more efficient use of the available bandwidth and a higher temporal resolution. Furthermore, since the system is working with the log of the photocurrent, a higher dynamic range is possible. Event based sensors have been used for navigation, localization, Shack–Hartmann wavefront sensing, and dynamic speckle analysis [13–15]. Here, we propose their use in CSI. This new data acquisition approach requires new algorithms to evaluate the stream of events as a signal. The goal of this article is to investigate the feasibility of this approach. In the next paragraph, the signal generation of event based interferometry is described, followed by suggestions to evaluate them. We describe the first, to the best of our knowledge, experiments using the Century Arks Silkyevcam [16] with an event sensor from Prophesee [9]. The first measurement results of a calibrated height step standard show the potential of the method.

In an ideal coherence scanning interferometer using an illumination source with Gaussian spectral distribution, the intensity in one pixel as function of the scanning position $z$ that is scanning an object at position ${z_0}$ is calculated according to the following formula:

The maximum of the contrast, which is the maximum of the envelope of the interference fringes, indicates the object position ${z_0}$.

The event based image sensor generates a signal when the log of the irradiance changes by an amount larger than a given threshold. The signal itself is a data package encoding the position, the timestamp, and the polarity of the change. The polarity of the change is 0 and 1 for the falling or rising signal. A set of events can then be described as

The size of the data package depends on the implementation of the camera. In our case, one event is encoded with 4 bytes with a minimum increment of the timestamp of 1 µs.

The event stream for a single camera pixel evaluated with the intensity generated by a spatial scan calculated with Eq. (1) is shown in Fig. 1. The simulation parameters were ${\lambda _0} = 532\;{\rm{nm}}$, ${L_c} = 5\;{\rm{\unicode{x00B5}{\rm m}}}$, and ${z_0} = 800\;{\rm{nm}}$, with a threshold value of 8% of the intensity of the reference. Each interference fringe shows as two groups of events representing the transition from the dark to the bright part of the fringe (red markers in Fig. 1) and vice versa (blue markers). The contrast of a fringe shows in the number of events in each group. Time can be attributed to the position according to the scanning speed during recording, which does not necessarily have to be constant, but it has to be known. Figure 1 bottom shows the integrated number of events over time. The object position ${z_0}$ is found in the center of the wavelet. The evaluation of an event based wavelet is strongly dependent on the event camera settings and will be discussed in more detail in a future publication. The first proof-of-principle results we show in this Letter have been obtained using the settings given in the Supplement 1, Table S1 and the following data evaluation algorithm: 1. Estimation of the center of the wavelet using the center of gravity (COG) of the events. 2. Identifying the falling and rising edges of the interference fringes using the polarity of the events. 3. ${z_0}$ is calculated from the average of the central rising and falling edge. Figure 1, inlet of the graph in the middle, shows the results.

 

Fig. 1. Top: Logarithmic intensity of the wavelet calculated with Eq. (1) with ${z_0} = 800\; {\rm{nm}}$. Middle: Extracted event stream by applying the thresholding to the intensity signal. Inset shows a magnification of the center of the wavelet and the results of the COG and phase evaluation. Red markers: rising signal events, blue markers: falling signal events. Bottom: Cumulative events.

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For the experiments, we used a custom-built Mirau type interference microscope to realize the eCSI, as shown schematically in Fig. 2. Its light source has a central wavelength of 532.0 nm and a coherence length of 4.0 µm. The Mirau objective lens is a Leica N-Plan NA 0.3 ${{20}} \times$. The event camera is the SILKYEVCAM from Century Arks using the Prophesee Gen3 event based image sensor with ${{640}} \times {{480}}$ pixels and a pixel size of ${{15}} \times {{15}}\;{\rm{\unicode{x00B5}{\rm m}}}$ [9,16]. Since there are no microlenses on the chip, the fill factor of a pixel is only 25%. The data is transferred via universal serial bus (USB) 3 interface to the measurement computer. For high precision scanning of the microscope, we used the nanopositioning and nanomeasuring machine NPMM-200 [17–19]. This laser interferometer controlled direct drive machine allows us to position a sample relative to a ZERODUR reference frame over a volume of ${{200}}\;{\rm{mm}} \times \;{{200}}\;{\rm{mm}} \times {{25}}\;{\rm{mm}}$ with a positioning resolution below 1 nm and continuous recording of the position and tilt of the sample. This basically eliminates the positioning uncertainty for our experiments. The eCSI sensor was mounted on the reference frame, as shown in Fig. 3. For a scan, the NPMM moves the test sample relative to the objective of the eCSI sensor. While scanning, the sample position is measured by the NPMM with a sampling rate of 8192 Hz.

 

Fig. 2. Optical layout of the eCSI system containing a Mirau type interference objective and an event based camera.

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Fig. 3. Measurement system containing the custom-built Mirau type interference microscope with the Silkyev cam in the nanopositioning and nanomeasuring machine NPMM-200 measuring the Halle depth calibration standard KNT 4080/03.

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We evaluated the eCSI principle on a depth calibration standard (Halle KNT 4080/03 [20]), specifically the groove with a calibrated height of ${{75.02 \pm 0.08}}\;{\rm{\unicode{x00B5}{\rm m}}}$. The measurement setup is shown in Fig. 3. The scan speed of the measurement was 25 µm/s. A video visualization of the captured events is shown in Visualization 1. The number of events captured by the single pixels of the camera is shown in Fig. 4. The timestamps were transformed to spatial distances with the monitored scanning speed and positions. For the evaluation, the events are processed individually for each pixel. This requires filtering the events of the pixel from the event stream. These are then processed according to the algorithm described above, yielding the height information ${z_0}$ for this pixel. Processing all pixels yields a height map, as shown in Fig. 5.

 

Fig. 4. Number of events captured by the event sensor. In the transition between the plateau and the groove, there were no events captured because the surface is too steep.

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Fig. 5. Measured height profile of the Halle depth calibration standard KNT 4080/03. The estimated height of our measurement is 74.954 µm, which is within the measurement uncertainty of the standard given as 74.94–75.10 µm (see Visualization 1).

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For a comparison of the data with the calibration data of the measured height standard, we removed the tilt of the data map in order to level the data by subtracting a best-fit plane minimizing the distance of the areas outside the groove to a plane vertical to the $z$ axis. The depth of the groove is then estimated as the difference between the averaged height information inside and outside the groove. A histogram of all measured height values is shown in the bottom part of Fig. 6 and in more detail in Fig. 7. The mean difference of the top and bottom part is 74.954 µm, which is within the measurement uncertainty range of the calibrated Halle normal, which is stated to be 74.94–75.10 µm. The FWHM of the measured height values is in the range of 30 nm. In the measurement of the upper level, there is a slight height difference between the two sides of the visible groove.

 

Fig. 6. Top: Cumulative events recorded by one pixel as a function of relative scan position. Bottom: Histogram of measured height values of all pixels for a measurement of the 75.02 µm groove.

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With a time resolution of 1 µs, current eCSI signal recording potentially offers scan speeds in the mm/s range and above. One limit in signal recording is the refractory period each pixel requires after an event has been recorded. For our experiments, this value was chosen to be 10.9 µs, which was not a limiting factor. The other limit is the maximum event bandwidth of the sensor: 50 mega-events per second (Meps). Whether or not this bandwidth is limiting strongly depends on the sample. It can be advisable to introduce a tilt so that the number of pixels in focus remains small throughout the scan. Future developments will allow much higher bandwidths: a sensor with 1066 Meps has been presented recently [21]. As stated above, signal evaluation of event based sensor data requires new approaches. In this Letter, we can merely give a first idea. As can be seen from the height measurement results, the presented algorithm works reasonably well. However, there are influence factors that still can be improved. As can be seen in Fig. 5, the algorithm filters out pixels primarily along some lines of the sensor. The reason behind this seems to be connected to the hardware. Our sensor has slightly varying thresholds for counting up and down, which leads in some regions of the sensor to a strongly asymmetric number of up and down events. Since our algorithm filters out edges that have less than two events, this leads to more invalid pixels in sensor regions with high threshold differences. Better hardware calibration by the vendor might be a solution.

 

Fig. 7. Left: Measured height values of the groove. The FWHM is 30 nm. Right: Measured height values of the top surface.

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In this Letter, we have shown that event based sensors can be used in CSI. This new detection scheme can help to overcome the major drawback of frame based interference intensity processing: the inefficient use of the available bandwidth. We have shown a first signal generation model and proposed a first algorithm for the height calculation from the events. With this algorithm and a Silkyevcam in combination with a custom-built Mirau type interference microscope in the NPMM-200, we measured a depth standard groove. The measured depth value lies in the measurement uncertainty region of the groove. These first results are promising and encourage the use of the new event based sensors in interferometry, potentially leading to higher measurement speeds in CSI.