2.1

Instrument principle/functioning

NanoCarb is an ultra-compact static Fourier transform imaging spectrometer developed for high resolution (R ~ 5000) and greenhouse gas spectroscopy. The instrument acquires an image of 60x60 pixels and the spectral information of each point of the image. An optic focuses the rays on the interferometer of the instrument composed of an engraved silicon slide and micro-lenses. The image is then decomposed into multiple small images of the same scene observed on the detector.

Each image is modulated by a Fabry-Perot interferometer which introduces a known Optical Path Difference (OPD) (Figure 1). And the most efficient way to acquire information on CO₂ is to acquire the interferogram only around this OPD. Then, spectral information of each point of the image is collected to find the CO₂ concentration. We use a particular method which is the partial interferometric sampling strategy, targeting information in Fourier space (this method is explained elsewhere by Gousset et al [3]).

The NanoCarb prototype shown in Figure 2 is developed in laboratory for a succession of characterization tests. A lens composed of prefocal optics is placed in front of the interferometer, which is itself placed in front of the detector, see Figure 4. The infrared SNAKE detector is cooled and temperature controlled. Each element of the instrument is individually characterized.

Figure 2.

Schematics of NanoCarb infrared prototype with prefocal optics masking observed field of view to avoid thumbnail overlapping and adapting scale of field of view to ImSPOC sampling

Figure 3.

NanoCarb Engraved silicon slide is placed in front of microlens array. Each microlens sees an unique spaced Fabry-Perot which make an annealed Fabry-Perot figure over series thumbnail of field of view (see Figure 1).

Figure 4

Sketch of optics for the Nanocarb instrument.

2.2

Interferometer description

Each Fabry-Perot interferometer is engraved in a silicon interferometric slide for CO₂ detection. The interferometer is the key element of NanoCarb technology. This innovative component allows us to perform both imaging and interferometry with a field of view of 18° and several interferometric samples in a snapshot. This technique permits us to optimize the SNR for a much reduced volume. This type of engraved structure permits to sample several interference states around one OPD. These interference states give us the essential information for the CO₂ measure or important geophysics/atmospheric parameter. That’s why the interferometric slide development is the key success factor of the instrument.

The very complex and unusual design of the interferometric component brings huge optical and technological challenges and requires the development of a digital performance model. In this model are inserted characterization step results and experimental calibration. We developed very precise characterization techniques to meet nanometer scale precision required on engraving slides.

2.3

Interferometric slides tolerances

These slides are manufactured with microelectronic techniques for silicon, but the unusual design of the slides requires the development of particular engrave method. We need interferometric slides with an optical quality, before and after engrave to insure (RMS tolerance values). That’s why we have to characterize the evolution of the intrinsic quality of silicon wafers with the engraving of the structure. A first tolerance is given on the absolute thickness of interferometer for which we want to optimize the sensitivity of CO₂ detection. The Figure 5 illustrates the knowledge of the mechanical thickness should remain in a 20 μm around 825μm.

Figure 5.

Jacobian of the CO₂ molecule is the sensitivity to a variation of CO₂ concentration of 1ppm. This jacobian is plotted along the width of interferometer. In red, the ideal silicon depth is comprised between 817μm and 835μm which seems to be not difficult to achieve.

In other hands, the irregularities of silicon surfaces have two main impacts:

3.1

Optical Coherence Tomography (OCT) characterization

We implemented a metrology mean for interferometric slides optical characterization. This characterization bench is Michelson interferometer used for OCT (Optical Characterization Tomography) interferential metrology technique. With this instrument we can characterize slides dimensions and silicon quality. The same equipment will serve also to calibrate instrument. Contrary to Classical OCT systems popularized by Huang et al. [4], the optical system in set in transmission arm just before detector. This configuration permits lot of characterizations from detector, optical componants such filter or interferometers up to whole instrument itself.

The characterization bench is in infrared configuration using the instrument detector itself, composed of several light sources such laser, DFB, SLED or tungsten lamp depending of type of tests, the Michelson interferometer separating the beam and the sensor collecting the recombined beam. The mobile arm of the Michelson interferometer is composed of a 100mm delay line that we can remote control. The delay line moving steps are precise on the nanometer scale; this allows us to make data acquisition with high spatial and spectral resolution.

Figure 6.

On the left: OCT characterization bench. On the right: Silicon slides placed in front of the infrared detector.

Indeed, our objective is to obtain very precise thickness map of the optical component. For that, we insert the silicon slides in the characterization bench, placed right before the sensor. The slides create two groups of interference fringes symmetrical about the optical contact fringes. The distance separating the two groups give us the slide thickness information. So we move the delay line around the two groups to introduce an optical path difference (OPD) and acquire the interferometric signal.

3.2

Data acquisition and processing

Thanks to a scan of the delay line, we acquire two interferograms on both slides of the optical contact, located of the two groups of fringes as shown on Figure 7. For each one, an image of the pupil is acquired at each step of the scan, with a typical λ/4 sampling of the fringes. Consequently, we obtain two cubes of data to process. The Figure 8 shows a raw acquired image for one of the two cubes, and the extracted interferogram over a region of the pupil.

Figure 7

Interferogram obtained after moving the delay line to the position corresponding to the OPD introduced by silicon slides.

Figure 8

Left: raw image of the pupil intensity, for a given position of the delay line. The silicon plate we scan is 500 nm depth engraved in a rectangular area. The image shows the two diffracted parallel edges of this area. Right: extracted interferogram from the green-circled area, as a function of the position of the delay line device.

The Figure 8 lets appear several illumination in-homogeneities over the pupil, cause by source speckles or dusts over the optics. We achieve a pre-processing of the data cube with a flat-normalization, as a result presented on Figure 9. Several fringes are visible, due to a tilt between reference line and delay line of the Michelson. This allows also to notice as expected a phase-shift across the frontier between engraved area and native area. We will explain now how we quantify this shift.

Figure 9

Normalized single image of one of the interferometric data cubes. The intensity variations over the image are due to interferences, introduced both by a tilt in the Michelson and by structure variations in the scanned silicon plate.

We extract the interferogram for each pixel of the pupil and then we process it. We combine two types of processing over the acquired data cubes:

The cross-spectrum method consists in a measurement of the phase above the intensity spike of the inter-correlation Fourier Transform, between a given pixel and a reference zone as presented on the Figure 10. We subtract the two obtained phase maps (for the two groups of fringes), to derive a relative phase map variations over the pupil, debiased of the bench aberrations.

Figure 10

Relative phase variation map obtained with the cross-spectrum method. The phase variations are given with respect to the reference position.

Nevertheless, we cannot derive an absolute thickness measurement of the plate with the cross-spectrum method. Furthermore, a plate structuration can induce some misestimate of the phase variation, because a continuity assumption is required for an un-wrap of the phase. For example, on the Figure 10, the 500nm-engraving is too important to un-wrap the phase with a continuity assumption, as a result of a misestimate of the depth.

Consequently, we jointly use envelope detection over each interferogram to read maximum value of both fringe group and its delay line corresponding position. By subtracting the two maps of position we obtain the absolute OPD above each pixel. This method is less accurate because we use the mechanical position returned by the delay line, as well as we use a centroid estimate over the envelope to derive the relevant thickness.

This absolute thickness is averaged over the different areas of the structured plate, and combined to the fine phase variation map as illustrated on Figure 10. The obtained map shows both nanometer-scale variations and large μm-structures.

The combination of the phase map and of the absolute OPD requires evaluating the mean wavelength of the source, while we need to assume the averaged optical index of the silicon to derive the mechanical thickness maps. The source wavelength is jointly evaluated on the Michelson by a Fourier Transform of the interferograms. Both this wavelength and temperature room are used to assume an effective optical index of the plate.

3.3

Obtained thickness maps

We present in this sub-section the obtained OCT maps of thickness. The sources of errors are assessed in characterization experiments. We measure two kinds of processed silicon samples:

OCT measurement results are presented on Figure 11. The absolute thickness measurement is 850 μm, for an 825 μm target. Joint mechanical measurements give 825 μm. A preliminary error budget analysis allows us to discard some experimental OCT biases. Some issue concerning constrains over the silicon during processing are investigated. Furthermore, the thinned plate presents a prismatic profile around 500 nm across the green line plotted on Figure 11. RMS values of the squared areas are reported in the Table 1. The squared are 64x64 pixels, comparable to NanoCarb thumbnail typical size. On the left full map, the RMS value is dominated by prismatic shape of the plate. A typical value of 10 nm is obtained remaining in tolerance budget in (p-v). We subtract the prismatic shape in the right-map, allowing to derive a RMS value around 1 nm => Thinned processing induces large variation over the plate, but has a good roughness. The observed structures over the right map seem to be induced by volumetric inhomogeneities of refractive index. We can note that it is more important for NanoCarb to measure a real optical thickness rather mechanical one.

Figure 11

Thinned silicon sample. Left: combined absolute thickness map. Right: fine OPD variations.

Table 1

RMS value of OPD variations, in unit of mechanical nanometer

Measured map in a first sample visible on Figure 12, showing an engraving around 380 nm for a target of 500 nm. A lithography issue is responsible for this bias, as well as a RMS value in the engraved area (square 2 3 and 4) around 10 nm compare to a 1 nm RMS value for the native area (1 and 5).

Figure 12

First engraved sample of silicon. Left: combined absolute thickness map. Right: profile of the absolute thickness map across the green line.

The second tested sample for the engraving technic is more promising as shown on Figure 13, with a closer 500 nm engraving area and a RMS value around 1 nanometer, comparable inside and outside the engraved area. Thus, the engraving process seems to not degrade the quality of the interferometer, with an accurate profile of depth.

Figure 13

Second engraved sample of silicon. Left: combined absolute thickness map. Right: profile of the absolute thickness map across the green line.