Monolithically Integrated Michelson Interferometer Using an InGaAs/InAlAs Quantum Cascade Laser at λ = 4 µm

Abstract

In the present article, we propose a monolithically integrated Michelson interferometer using a λ = 4 µm InGaAs/InAlAs quantum cascade (QC) laser as the light source. By using simple fringe detection and a four-point interpolation on each fringe, we will be able to detect minimal object displacements of 500 nm—corresponding to 25% of half the laser emission wavelength. Such an interferometric photonic integrated circuit has interesting applications for precision computerized numerical controlled machines. Since the industrial standard of such machines currently consists of glass-based linear encoders with a resolution of 5 µm, our interferometer-based system will enable an improvement of at least one order of magnitude.

1. Introduction

The first modern interferometer experiment was carried out by A A Michelson in the year 1881 [1]. However, since the quite long and relatively thin arms of this optical apparatus tended to vibrate even under very careful handling, A A Michelson fabricated and characterized an improved version of his interferometer in 1887. The corresponding measurements were carried out together with E W Morley—using (in principle) the same experimental configuration as six years earlier [2]. However, in this second, much more stable experiment, the entire optical instrumentation was literally “floating” on a big trough filled with liquid mercury. With this important work, the two researchers invented, built, and characterized the optical interferometer that bears their names until today. The goal of these experiments was to precisely measure the velocity of the Earth relative to the “luminiferous ether”—the hypothetical medium that was supposed to “carry” the electromagnetic waves. However, the “Michelson-Morley experiment” (as it is referred to today) resulted in a relative velocity of zero (v_rel = 0); therefore, it unambiguously proved the non-existence of the luminiferous ether. Electromagnetic radiation can, therefore, also propagate in a vacuum, for example, in space. The experimental realization of the seminal work of A A Michelson and E W Morley is shown in Figure 1 below. Just about two decades later, the surprising outcome of this research effort contributed to A Einstein’s special theory of relativity, within which he postulated that the speed of light is a “universal natural constant”, meaning that it is independent from the observer’s relative velocity [3,4].

Much more recently, Michelson interferometers have made their way into industrial applications such as high-precision positioning [5] or distance measurements [6]. Successful approaches include the glass-based device of Jestel et al. [7] and the silicon-based interferometer of Ulbers [8]. In 2006, fiber optic Michelson interferometers were demonstrated as well [9,10]. However, although most of these devices were already using an integration of several optical components on a single substrate, they did not include an integrated light source or laser. A little bit later, a research group from Japan successfully developed the world’s first monolithically integrated GaAs-based Michelson interferometer, including a laser light source, in 1995 (Suhara et al. [11]).

This research group managed to even integrate a grating coupler for a collimated surface-emitting sensor beam. As another particularly advanced example, we would finally like to refer to our own work from 1995, in which we successfully fabricated and characterized a monolithically integrated interferometric displacement sensor [12]. In its most mature version, this semiconductor device consisted of a distributed Bragg reflector (DBR) laser, two optical phase modulators, two photodetectors, two directional couplers, and the optical waveguides connecting them. Suitably combined with each other, these components were arranged as a double Michelson interferometer for relative optical distance measurements [13].

Within the last couple of years, such Michelson interferometers have been used for new, very interesting applications. Amongst others, these actually include mechanical engineering or astronomy. As one example, this is illustrated by a paper written in 2023 by Englert et al., in which wind velocities and directions in the Martian atmosphere have been determined [14]. Very recently, Michelson interferometers have also been utilized for exact failure location in extended optical fiber networks [15], high-resolution fiber optic sensor readout systems [16], detecting small volume/low concentration chemicals in a ring cavity laser [17], and absolute distance measurements using frequency combs [18,19], as well as tracking impact locations with a low-coherence Michelson interferometer [20].

In the article presented here, we propose the fabrication of a device with a very similar architecture to the one described in reference [13]. However, since the alignment of the externally moving mirror in a visible wavelength Michelson interferometer (such as the version from the year 1995/96) is not at all trivial—especially because of the small waveguide dimensions—here, we suggest the use of a mid-infrared quantum cascade (QC) laser emitting radiation at a wavelength of 4 µm. After the first demonstration of such a QC laser in 1994 [21] and the first successful room temperature CW operation in 2002 [22], these devices have now reached a high degree of maturity, finally allowing their use in ultra-stable optical interferometry. In comparison to our previously fabricated interferometer circuit, however, the five-times longer laser wavelength will obviously result in a five-times lower (coarser) measurement resolution. However, compared to most glass scale linear encoder measurement systems of industrial high-precision, computerized numerical control (CNC) machine tools, a factor of 10 (500 nm instead of 5 µm) will be gained [23]. When finally looking at the already existing interferometric measurement systems used in such CNC machines [24], the integrated optical approach suggested here will not only guarantee considerably improved measurement precision but will also greatly reduce both the physical dimensions and the alignment needs of the entire unit. As shown in Figure 2 below, the typical dimensions of existing interferometric systems are in the 25 cm (or 10 inches) range; the proposed monolithically integrated interferometer alone is going to occupy an area on the order of 5 × 2 mm², along with a thickness of 250 µm. Together with the required electronics, temperature stabilization, and the laser driver circuit, a small housing with a side length of 5 cm in the largest dimension can be envisaged.

Last but not least, the proposed optical interferometer chip in its small, sealed housing can eventually be connected to external measurement electronics by a couple of soft data cables and optical fibers. This will result in a higher degree of flexibility and less critical space requirements. Compared to a bulky interferometric setup, such a monolithically integrated system is, therefore, going to profit from greatly improved stability and reduced alignment requirements.

2. Materials and Methods

In the following section, we are going to describe the required layer structure in a more detailed way. First of all, it is obvious that due to the highly demanding application of precise optical displacement measurements, the wavelength stability and positioning reproducibility of our device can only be guaranteed by using a single-mode optical laser light source. Therefore, this laser (the crystal growth of which is performed by molecular beam epitaxy) must be of the distributed feedback (DFB) or distributed Bragg reflector (DBR) types. Similar to a published QC laser in the 4.3 µm wavelength range [25], the layer structure is shown in

Table 1. Generic layer descriptions, materials, thicknesses, and doping levels of the proposed Michelson interferometer.

Layer Descriptions	Materials	Thicknesses	Doping Levels
Cap layer	InP	0.5 µm	Si, 2 × 1019 cm−3
Upper clad	InP	1.8 µm	Si, 2 × 1017 cm−3
Grating	In0.53Ga0.47As	0.2 µm	Si, 5 × 1017 cm−3
Upper waveguide	In0.53Ga0.47As	0.3 µm	Si, 8 × 1016 cm−3
Active region	In0.68Ga0.32As/In0.39Al0.61As	1.4 µm	Si, 1 × 1017 cm−3
Lower waveguide	In0.53Ga0.47As	0.3 µm	Si, 8 × 1016 cm−3
Substrate	InP	−	Si, 6 × 1016 cm−3

.

Starting from the injection barrier, one period of the active region consists of the following layer sequence. In

Table 2. Type of epitaxial layers, along with the materials, thicknesses, and doping levels for 1 of the 30 totally active region periods [25,26].

Layer Descriptions	Materials	Thicknesses	Doping Levels
Barrier 1/QW 1	In0.39Al0.61As/In0.68Ga0.32As	41 Å/10 Å	−
Barrier 2/QW 2	In0.39Al0.61As/In0.68Ga0.32As	15 Å/39 Å	−
Barrier 3/QW 3	In0.39Al0.61As/In0.68Ga0.32As	15 Å/34 Å	−
Barrier 4/QW 4	In0.39Al0.61As/In0.68Ga0.32As	16 Å/31 Å	−
Barrier 5/QW 5	In0.39Al0.61As/In0.68Ga0.32As	23 Å/23 Å	−
Barrier 6/QW 6	In0.39Al0.61As/In0.68Ga0.32As	18 Å/20 Å	−
Barrier 7/QW 7	In0.39Al0.61As/In0.68Ga0.32As	19 Å/18 Å	Si, 1 × 1017 cm−3
Barrier 8/QW 8	In0.39Al0.61As/In0.68Ga0.32As	20 Å/17 Å	Si, 1 × 1017 cm−3
Barrier 9/QW 9	In0.39Al0.61As/In0.68Ga0.32As	22 Å/16 Å	−
Barrier 10/QW 10	In0.39Al0.61As/In0.68Ga0.32As	22 Å/15 Å	−
Barrier 11/QW 11	In0.39Al0.61As/In0.68Ga0.32As	29 Å/15 Å	−

(below), all thicknesses are given in Å, the thicknesses of the barrier layers are given in bold, the QW layers are shown in roman numerals, and the n-doped layers are underlined. In order to accommodate an inter-subband transition energy as large as 310 meV, strain-compensated material (±1.2%) has to be used.

The main vertical inter-subband transition of this layer structure takes place at the desired energy, corresponding to a wavelength of 4 µm. In order to generate optical output radiation with a sufficiently small spectral linewidth and, thus, reasonably large coherence length, a single-mode light source is needed. The fabrication of this light emitter was, therefore, based on an optical diffraction grating defined at the interface between the top waveguide and the upper cladding layer. In order to perform dry etching of this diffraction grating, the epitaxial growth process needs to be interrupted after the top waveguide layer. For the fabrication of the grating, holographic exposure of a sufficiently thin photoresist layer using a two-beam interference setup (as described in reference [27]) is performed. Afterward, Cl₂-based, inductively coupled plasma (ICP) etching is used to transfer the grating structure into the semiconductor [28]. With this technique, low etch damage, along with precisely vertical sidewalls, can be achieved. The first point is especially important because there will be an epitaxial regrowth after grating fabrication. A typical picture of the resulting grating before epitaxial regrowth with a period of Λ = 0.58 µm is shown in Figure 3 below [29,30]. As mentioned before, the 1.8 µm thick InP-based upper cladding and the highly n-doped 0.5 µm thick final cap layer will then be re-grown on top of the grating. Very similar devices are commercially available, for instance, from Alpes Lasers SA in St. Blaise (NE), Switzerland [31] and from DRS Daylight Solutions in San Diego, CA, USA [32,33].

For the definition and etching of the waveguide structures, standard photo-lithography, followed by a dry-etch process based on Cl₂-chemistry, is used. The etch depth is supposed to reach slightly deeper (t = 5 µm) than the total epitaxial layer thickness of 4.5 µm. The wafer is then covered with a 200 nm thick Si₃N₄ electrical isolation layer. After the dry-etched opening of the electrical contact areas, the Ti/Au (10/500 nm) top metal layers are lift-off deposited. After bottom metallization Ge/Au/Ag/Au (10/25/50/350 nm), the cleaving of rectangularly shaped individual interferometer chips of 5 × 2 mm² in size is performed.

3. Results

In the upper half of Figure 4, a microscope image of a Michelson interferometer—fabricated in 1996 using GaAs/AlGaAs technology—for a wavelength of λ = 0.82 µm is shown. In the lower part of Figure 4, a schematic drawing of a similar Michelson interferometer—as it was fabricated in this experiment—is presented. The only external element added to this integrated Michelson interferometer is a gradient index (GRIN) lens [34]. It is attached to the waveguide of the central output beam (sitting between the two phase modulators). Such GRIN lenses are not yet very common for the mid-IR wavelength range, yet there are several reports available in the scientific literature. Although such an element is not absolutely mandatory, its use nevertheless facilitates both interferometer alignment and operation [35].

In contrast to the experiment in 1996, the light source is a continuous-wave-operated DFB quantum cascade laser at a wavelength of 4 µm. As can be seen on the datasheet of such commercially available DFB lasers, linewidths of the order of ∆ν = 3 MHz are typically observed. This value corresponds to a coherence length of L_coh = c/(π∆ν) ~ 30 m. Regarding the use of such a device for optical displacement measurements in CNC milling machines, the required maximum readings of 2 m can be achieved without any problem. In other words, assuming (for simplicity) a Gaussian linewidth profile of our laser source, the contrast of the corresponding interference fringes will show similar Gaussian decreasing behavior. At an equal length of both the reference and signal arms—corresponding to a vanishing relative mirror displacement—a maximal fringe contrast of m = 1 is seen. Going to a relative mirror displacement of ΔL = ±1 m then results in a very slight reduction in the contrast (m = 0.92) only.

On both sides adjacent to the single-mode DFB laser light source, two photodetectors labeled ‘Photodetector 1’ at the top and ‘Photodetector 2’ at the bottom are shown [36]. In order to opto-electronically isolate the active region of the laser and the two photodetectors, optical isolation trenches with a depth of twice the ridge waveguide height were etched. The 1996 experiment revealed the clear necessity for this additional feature. Otherwise, the photocurrent due to the optical crosstalk between the laser light source and the nearby photodetectors will quickly exceed the actually interesting interferometer signal by an order of magnitude. The digital photograph at the top of Figure 4 was made from an integrated Michelson interferometer using a DBR laser, and in the schematic drawing at the bottom, a DFB laser is proposed. It becomes clear from several publications in the scientific literature that a DFB laser profits from increased wavelength stability and considerably lower sensitivity against optical feedback effects. This is true even for a butt-joined DFB laser/waveguide pair, as was successfully demonstrated in reference [37]. When using (such as in 1996) a DBR laser, the only optical isolation against such unwanted feedback effects consists of a relatively strong diffraction grating. However, there existed no other design-inherent isolation; the correct functioning of the measurement chip was, therefore, based on a small amount of light (~10%) to be coupled out. Due to the inherent beam divergence in free space, there was, again, only ~10% found its way back into the laser. Slight deviations from the ideal coupling ratio might finally have resulted in another factor of 10%. The multiplication of these three small amounts resulted in sufficiently tiny feedback into the DBR laser. As a result, a relatively good beam quality, optical linewidth, and coherence length could be maintained.

Table 3. The waveguide dimensions and several specific device parameters of the components in this work.

Component	Width	Length	Loss	Separation	Splitting	Sensitivity	Responsivity
Waveguide	8 µm	5 mm	1 cm−1	−	−	−	−
DFB-Laser	8 µm	500 µm	10 cm−1	−	−	−	100 mW/A
Directional Coupler	8 µm	450 µm	1 cm−1	4 µm	50%/50%	−	−
Phase Modulator	8 µm	800 µm	1 cm−1	−	−	−	−
Photodetector	8 µm	500 µm	10 cm−1	−	−	10 mA/W	−

below contains the extrapolated device parameters for each single component of this interferometer. Both waveguide width and separation are four times as large as in typical 820 nm laser diodes. Laser responsivity and detector sensitivity were taken from the previously mentioned publications [13,23].

The schematic drawing in the lower half of Figure 4 shows an integrated optical Michelson interferometer operating at 4 µm. Given a waveguide width of 8 µm, contact lengths between 500 and 800 µm, and a (larger) curvature radius of 1 mm, a chip size of 5 × 2 mm² is envisaged here. The exact length of the directional coupler (ideally acting as a 50/50% beam splitter and working with TM (instead of TE)-polarized light) will have to be either numerically simulated or experimentally determined. For the time being, a tentative length of 450 µm is proposed. The gap between the two waveguides of the directional coupler should become roughly 4 µm. Another interesting question concerns the optimum geometrical dimensions and the absorption properties of the optical waveguides, the photodetectors, and the phase modulators. Their most critical parameters will ideally be defined by fabricating three different lengths, widths, or coupling strengths. Experimental measurements will then allow us to determine the most suitable device dimensions for each component. When assuming a CW QC laser output power of 100 mW, a QC detector sensitivity of 10 mA/W, a waveguide loss of 1 cm⁻¹, a directional coupler efficiency approaching 10%, and input/output efficiencies of the order of 10% in each case, then a total AC signal amplitude of 1 µA can be expected.

For a diode laser based on an interband transition, the bias applied on the active device will—via a pronounced quantum-confined Stark effect (QCSE)—result in a smaller transition energy than in the passive, unbiased areas. The energy of the emitted photons in the lasing area is, therefore, no longer sufficient to be absorbed in the unbiased waveguide area. This behavior was first described by D A B Miller et al. in 1984 [38]. The situation is, however, the opposite for the case of a laser based on an inter-subband transition. When an electric field is applied to such a QC laser-active region, the Stark shift results in a larger inter-subband transition energy [39,40]. If there were step-shaped absorption behavior, such as in a diode laser, the emission would, therefore, be strongly absorbed in the unbiased waveguide areas. However, unlike inter-band transitions, inter-subband transitions (such as in our case) exhibit peaked (i.e., not step-shaped) absorption. A biased ISB laser section will, therefore, shift its emission peak toward a slightly larger transition energy (red/black curves in Figure 5 below) than the absorption peak of the unbiased waveguides (blue curve in Figure 5 below). For a sufficiently small full width at half maximum (FWHM) in the ISB luminescence/absorption peaks (for instance, with an FWHM of 15 meV)—along with a large enough energy difference between the emission and absorption peaks—the mutual overlap between the biased laser/photodetector and unbiased waveguiding areas gets low enough to result in a small waveguide loss. An estimated loss value of α_WG = 1 cm⁻¹ then leads (after a 10 mm total path length (5 mm back and 5 mm forth) within the interferometer) to 37% of the initial intensity. At the same time, the unaltered high spectral overlap between laser emission and photodetector absorption will result in efficient absorption in the photodetecting section.

Within its linear range for an applied electric field of E = 0.32 V/47.8 nm = 6.7 × 10⁴ V/cm—according to reference [41,42]—the phase modulator (which is based on the QCSE) produces a refractive index change of ∆n = 1.0 × 10⁻³. In order not to overly stress the semiconductor material used, we work here—somewhat arbitrarily—with the known maximal field value being present in the active quantum cascade laser section [43,44]. With the above change in the refractive index, we can define a sufficiently long phase modulator to result in an optical phase shift of π/2 (i.e., π/4 per single pass). This condition is called phase quadrature. In order to calculate the required length of the modulator, let us first consider the angular argument of an electromagnetic wave having a wavelength of λ = 4.0 µm. Here, k_λ is the wave vector defined by k_λ = 2π/λ. We then compare the angular argument produced by a phase modulator with length L and having either a refractive index of ‘n’ or ‘n + Δn’. A refractive index of ‘n’ corresponds to an applied voltage of 0 V, and a refractive index of ‘n + Δn’ is seen at a maximum applied voltage of −10 V. Therefore, we obtain the following:

$$\Delta \mathsf{\phi }\left[\right(\mathrm{n}+\Delta \mathrm{n})-(\mathrm{n}\left)\right]{\mathrm{k}}_{\mathsf{\lambda }} \mathrm{L}=\Delta \mathrm{n} {\mathrm{k}}_{\mathsf{\lambda }} \mathrm{L}$$

(1)

$$\Delta \mathsf{\phi }=(2\mathsf{\pi } \Delta \mathrm{n} \mathrm{L})/\mathsf{\lambda }$$

(2)

In addition, values of $\Delta \mathsf{\phi }$ = π/4 (π/2) for the desired single-pass (double-pass) optical phase shift, ∆n = 1.0 × 10⁻³ for the refractive index change within the linear range of Figure 5, $\mathsf{\lambda }$ = 4 µm for the wavelength of the DFB laser, and k_λ = 1.5707 µm⁻¹ are used [45]. With these parameters, Formula (2) can be solved for the yet unknown length, L, of the modulator:

$$\mathrm{L}=(\mathsf{\lambda } \Delta \mathsf{\phi })/(2\mathsf{\pi } \Delta \mathrm{n})=\Delta \mathsf{\phi }/({\mathrm{k}}_{\mathsf{\lambda }} \Delta \mathrm{n})$$

(3)

By using the above parameters, we obtained a value of L = 500 µm. Including a safety margin, we get L = 800 µm. In addition to its good manufacturability, this length still results in relatively low waveguide losses. Apart from the explicit calculation in Equation (2), most of the other results presented in this section are based either on numerical simulations or on experimental variations. In Figure 6, the signals of the two photodetectors located to the left and the right side of the DFB laser, respectively, are presented. The externally moving mirror travels roughly 10.5 µm in total between two extreme positions, which are 5.25 interference fringes apart.

The two discontinuities (red arrows) indicate the changes in direction of the external mirror. In addition to the current traces of the two interferometer signals in phase quadrature in Figure 6, these two signals will also be presented in the form of a so-called Lissajous figure. This more intuitive plot of the two measurement signals is shown in Figure 7. One interferometric fringe corresponds to half the employed laser wavelength; thus, it corresponds to 2 µm. Already, a minimal interpolation of four points per interference fringe (minimum, maximum, and two zeros in between) of this movement results in a measurement resolution of 500 nm. In Figure 7, we show the expected Lissajous figure of the sinusoidal/co-sinusoidal oscillations shown in Figure 6. For a mirror displacement in a given direction, the phasor of this roughly circular graph will turn in clockwise direction. If the sense of the mirror movement is reversed, the phasor in the Lissajous figure will turn in counter-clockwise direction accordingly.

Although the expected measurement resolution of 500 nm is five times lower (i.e., worse) than in our GaAs-based Michelson interferometer from 1996, it is still better than the presently used glass scale linear encoders by a factor of 10.

As shown in our earlier experiments from 1996, it is obvious that a shorter wavelength laser would—at least theoretically—allow for a considerably better measurement resolution. However, we must take into account the rather harsh environmental conditions typically prevailing in a mechanical workshop. They include oil vapors, metal chips, vibrations, and considerably large temperature changes. Under these somewhat difficult conditions, looking for a resolution far below 1 µm seems not to be very useful and rather overkill, resulting (eventually) in an increased number of problematic technical issues rather than satisfactory positioning precision. As an important difference to the results of 1996, the experiments suggested here are not made under idealized laboratory conditions or during vibration-free night hours. This easily explains why the relative resolution normalized by the laser wavelength has become five times lower.

Of course, knowledgeable people in the field might ask why mid-IR QC lasers have not been used much earlier for monolithic interferometers, especially since they were demonstrated already back in 1994 [21]. As a matter of fact, the first QC lasers were available only as cryogenically cooled devices. Room temperature CW operation with threshold currents in the several hundred mA range was achieved in 2002 [22]. True low-threshold currents have only been available since 2016 [46].

4. Discussion and Most Suitable Applications

In this publication, we propose the use of a monolithically integrated Michelson interferometer for optical displacement measurements—employing a QC DFB laser at an emission wavelength of 4 µm. Compared to existing interferometers that utilize near-infrared lasers at λ = 820 nm, this wavelength—and thus the resolution of the entire sensor circuit—will be coarser by a factor of five. However, in the main envisaged application (interferometric position measurement in CNC machine tools), the currently employed resolution will nevertheless be improved by roughly a factor of 10. Today, such machines typically use glass scale linear encoders, with a standard accuracy of 5 µm, whereas by using the interferometric method suggested in this publication, a positioning accuracy within 0.5 µm (i.e., 500 nm) will become possible. In Figure 8a, the existing measurement scheme based on such a glass scale linear encoder for current industrial applications is presented; Figure 8b shows a short section and enlarged details of such a linear encoder.

As written above, the linear accuracy of this very well-established positioning system is around 5 µm. In the following section, we will see how this accuracy can be improved by the use of an optical interferometer.

As mentioned before, very rough interpolation results in at least four points per period, i.e., a resolution of 500 nm. The arguments behind this number are based on the fact that the fringe distance corresponds to exactly one-half of the laser wavelength of 4 µm. Furthermore, by assuming that four points per fringe can be easily detected (the minimum, maximum, and two zeros of the sinusoidally modulated signal), we obtain a resolution of one-quarter of half the laser wavelength used. Although this resolution is five times ‘worse’ than in our GaAs-based Michelson interferometer from 1996—relative to the laser wavelength—it is still a factor of 10 better than the presently used glass scale linear encoder systems. In any case, it is clear that standard fabrication procedures and tolerances in mechanical workshops rarely reach below 10 µm. From this point of view, a positioning accuracy of 500 nm will be a really important step forward. Working with an even higher accuracy would, however, be truly overkill; parasitic effects, such as thermal and mechanical instabilities, in CNC machine tools would inherently prevent the successful implementation of such ultra-high positioning precision.

When finally looking at measurements in quantum metrology and investigating either entangled photons or detecting gravitational waves, due to its semiconductor laser light source, the suggested Michelson interferometer constitutes an emitter with too low spectral purity. With the proposed semiconductor-based interferometer having a typical coherence length of 30 m, the small effects in such highly specialized applications are simply not accessible.

5. Specific Use in Modern CNC Machine Tools

In today’s CNC machines (both for measuring and production purposes), high-precision positional readings based on glass scale linear encoders have been the industrial standard for several decades already. Such reading systems can be found, for instance, in DMG MORI AG milling machines. These machine tools are fabricated at the former Friedrich Deckel AG, Munich. One example of such a milling machine is shown in Figure 9 below.

Glass-based encoding systems—such as the one shown in the previous example—have a maximal accuracy of 5 µm. This has to do with mechanical ruggedness, temperature instabilities, and the smallest manufacturable feature size on such glass rulers. However, apart from mechanic CNC machines, glass scale linear encoders, such as the one in Figure 8, can also be found in metrology systems equipped, for instance, with the PICOSCALE Sensor Head of SmarAct, Inc. [48]. After all, there are numerous applications where a higher precision of the positional reading would be a clear advantage. In addition, the physical dimensions of the existing systems can no longer really be shrunk: a glass scale linear encoder with its tiny inscriptions needs a certain physical dimension, which corresponds pretty much to the maximal travel of the corresponding machine axis. If one could replace this bulky ruler element with a low-cost and touchless interferometer-based solution, this would be a formidable advantage. The interferometer proposed in this article is not overkill in terms of precision—owing to its long wavelength laser light source. Thanks to adequate housing, it will not be sensitive to oil vapors, metal chips, or other types of typical dirt that are generated in a mechanical workshop environment. With its factor-of-10 improvement of the expected accuracy, it constitutes a true improvement compared to existing glass scale linear encoding systems.

6. Use for Absolute Distance Measurements

The spectrometer presented in this publication also has the potential to be used as an absolute distance sensor. One method of choice for this purpose is frequency-modulated continuous-wave (FMCW) light detection and ranging (Lidar) [49]. With this method, a frequency-chirped, continuous-wave laser produces reflected waves from mirror-like surfaces. The required optical frequency shift is generated by an acousto-optic modulator. The aliasing-free beat signal produced by this method can then be used to extract the absolute distances of mirroring objects. As a rather advanced example, experimental demonstrations resulted in values of v = 26.43 ± 0.037 m/s for the velocity of a spinning disk at a distance of 1.267 ± 0.016 m. Furthermore, the system proposed in reference [44] above is capable of discriminating the direction of rotation based on a single fast Fourier transform analysis. In addition, a three-dimensional image of such a spinning disk can be reconstructed.

7. Conclusions

Resembling our earlier results from the year 1996 from using a GaAs-based monolithically integrated Michelson interferometer for optical displacement measurements, we propose a very similar device but with a five-times larger laser emission wavelength of 4 µm instead of 820 nm. For the typical applications envisaged here—namely, positional sensing in CNC machine tools—the resulting resolution when using mid-infrared light is still sufficiently high for most problems occurring in a mechanical workshop. As another important difference to the device demonstrated in 1996, a DFB laser instead of a DBR laser will be used. This results not only in a more straightforward fabrication procedure but also allows for more efficient optical isolation between the single-mode light source and the downstream interferometric circuit. This is an important issue because the GaAs-based displacement sensor from 1996 clearly ran into the problem of too high optical feedback entering into the DBR laser. This feedback led to a greatly increased laser linewidth and, thus, a much shorter coherence length of the DBR laser light source. In practical terms, this meant that our sensor could not be used for mirror distances larger than about 50 cm; in a typical mechanical CNC machine tool, such maximal mirror displacement would be clearly insufficient. With the suggested improvements, typical maximum displacements of ±1 m will be possible without problems. Obviously, the proposed interferometer will be suitable for any other high-precision measurement at the accessible distance range.

8. Patents

Since none of the contributing authors is currently working in the area of optical interferometry, there are no patent issues associated with this research.