1. Introduction

Spectrometers are essential analysing instruments used in a wide variety of different application fields. Typically, a conventional spectrometer involves a complex system of separated imaging components and a dispersive element mounted on a scanning unit. In practice these spectrometers are often bulky and mostly limited for laboratory use.

Meanwhile the need for compact instruments suitable for in-line process control to measure quantities such as color, content and concentration becomes more and more important in fields such as pharmacy, biotechnology, chemistry, printing industry, agriculture-food or glass manufacturing industry. Especially for these applications a miniaturization of spectrometers is often required whereas simultaneously the optical performance in efficiency, spectral bandwidth and resolution of the instruments has to be guaranteed.

In the last years, different set-ups of micro- and miniature spectrometers have been introduced [1–5], offering a small volume concept but otherwise show performance limitations in resolution, spectral bandwidth and numerical aperture or sometimes are relatively complex and difficult to manufacture in volume.

An appropriate approach to decrease the volume of a spectrometer is based on the concept of diode array spectrometers. In this type a complete spectrum is recorded simultaneously and moving parts became superfluous. Additionally the combination of imaging and dispersive properties in the single element of a concave grating reduces the number of optical units used in the system. The performance of the concave grating is the most determining factor of this spectrometer type. To manufacture these gratings a recording process based on interference lithography (IL) is suitable. For IL also the term “holography” is in use. In comparison to other manufacturing technologies, the advantage of properly realized holographic gratings is that they are completely free of both, the small periodic and the random groove placement errors which ensure minimum disturbing stray-light. Additionally IL allows the realization of gratings with periods of high spatial frequency, thus providing sufficient spectral image dispersion without a large projection distance and an adapted profile geometry offering high diffraction efficiency.

The recording process of concave gratings requires two coherent point sources providing diffraction limited spherical waves. In the intersection region of the spherical waves an interference pattern is created which is recorded into a sensitive photo resist. An essential aspect in the lithography process is the positioning of the two point sources with respect to each other and to the recording substrate. To fulfil the optical requirements, usually the two point sources are realized by perfectly adjusted mirrors, pinholes and two separated lens systems with diffraction limited quality. Here, due to the volume of the recording lens systems the minimum distance between the two point sources is limited which restricts the specifications of the spectrometer concept in terms of diffraction angle, numerical aperture, selected diffraction order and minimum diameter of the concave grating.

In this paper we present the concept, the realization and the application of an imaging spectrometer covering an optical volume of 11 × 6 × 5 mm³. The instrument is based on a multi-order concept and offers a spectral range of 400 – 1030 nm, and a 5 nm resolution. The numerical aperture of NA = 0.2 allows a high energy efficiency. As the most essential element, a concave diffraction grating with a diameter of 5 mm and an image distance of 8.6 mm was manufactured in a holographic recording process. To provide the two high quality point sources in close proximity necessary for the recording process, a supplementary hologram was fabricated and integrated in the final recording configuration.

2. Spectrometer conception

In the conception of a compact optical spectrometer, the most challenging part in the optical design is to optimize simultaneously the competing demands of high spectral resolution, large spectral bandwidth and miniaturization of the required volume. Generally, the optimization of one property will reduce the qualities of the other quantities. In miniature systems the demand for small apertures introduces an additional difficulty.

To simultaneously realize all performance demands, we chose a multi-order spectrometer concept [7] which is shown schematically in Fig. 1. Here, the complete spectral bandwidth is not recorded in a single step but by the subsequent focusing of adjacent partial spectral intervals in different diffraction orders into the image plane. Therefore the concept requires sequential illumination of the target with light sources of neighbouring and limited spectral ranges [e.g. by using light emitting diodes (LEDs)].

 

Fig. 1. Scheme of the miniature multi-order spectrometer showing the working principle. The light which is coupled into the spectrometer via the entrance slit is dispersed and imaged by the concave grating. In dependence on the specific diffraction order a different wavelength range is focused on the detector.

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Fig. 2. Optical layout of the miniature multi-order spectrometer. The spectrometer covers an optical volume of 11 x 6 x 5mm³. Due to imaging multiple higher diffraction orders, the concave diffraction grating is significantly tilted with respect to the optical axis. The spectrometer offers a numerical aperture of NA = 0.2

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Figure 2 shows the optical design of the realized spectrometer set-up, comprising the entrance slit, the concave grating and the detector surface. The concave grating accomplishes the tasks of both the dispersive and the focusing element. This simplified system design allows a compact and sensitive instrumentation. The object distance ranging from the entrance slit to the center of the concave diffraction grating is L₁ = 8.8 mm and the image distance is L₂ = 8.6 mm. Based on the set-up principle of imaging multiple higher diffraction orders, the concave diffraction grating is significantly tilted with respect to the optical axis. The grating shows a diameter of D = 5.0 mm and a radius of curvature of R_s = 9.039 mm. The addressable detector length covers a lateral extension of 1 = 3.7 mm. The spectrometer offers a numerical aperture of NA = 0.2 which is relatively large in relation to comparable miniaturized spectrometers. The considerable large numerical aperture guarantees a near-perfect, aberration minimized imaging and therefore a maximum spectral resolution only for a limited angle distribution and for a narrow spectral bandwidth. The multi-order principle allows an extension of the bandwidth of the sensor. For each diffraction order the related spectral range is transferred by the total numerical aperture of the imaging system which guarantees an optimized spectral resolution. For example Fig. 2 shows the ray trace of the 9^th diffraction order which covers a spectral range between 515 nm and 572.2 nm.

To cover the complete wavelength range without spectral gaps it is essential to guarantee that the successively detected spectral intervals which are correlated to particular diffraction orders are directly attached to each other.

During the sequential recording of the adjacent spectral intervals the physical width of the detector array remain unchanged but the extension of spectral width of the intervals decreases with decreasing wavelength range and increasing diffraction order.

Let m be the integer value of the minimum diffraction order which images the interval covering the maximum wavelength onto the detector array. In this m^th diffraction order the minimum and maximum wavelength detected by the array are λ_m,min and λ_m,max respectively and the correlated spectral bandwidth Δλ_m of the interval is difference between both: λ_m,min = λ_m,max + Δλ_m.

The necessity to cover the entire spectrum and to omit a spectral gap leads to the continuous condition which demands that the minimum wavelength detected by the order m is equal to the maximum wavelength detected by the next higher order m+1:

Additionally, the maximum wavelength λ_m,max for the m^th diffraction order and the maximum wavelength λ_m+1,max for the (m+1)_th diffraction have to be detected by the same pixel or equivalent position of the detector. In our set-up this position is covered by the pixel which is closest to the entrance slit. Following the grating equation the diffraction angle for different wavelengths remains unchanged when the product of diffraction order and wavelength is constant. The fulfilment of this requirement guarantees analogous imaging behavior for the different wavelength in the related diffraction order. This geometric aspect leads to:

From the combination of both equations it is possible to derive the bandwidth Δλ_m as a function of the maximum detectable wavelength and the minimum detectable diffraction order

The extension of this method to the higher diffraction orders (m + n) allows a more general consideration. Also here the related continuous condition must hold:

Here Δλ_m+n is the spectral bandwidth of the (m+n)^th diffraction order. In an analogous way also the relation for the spatial position is applicable:

The combination of the Eqs. (4) and (5) leads to:

The subtraction of the successively following spectral intervals from the basic maximum wavelength λ_m,max are determining the maximum wavelength for the (m+n)^th diffraction order:

From the combination of the relations (5), (6) and (7) follows the spectral bandwidth Δλ_m+n for the (m+n)^th diffraction:

The last relation shows, that the relevant spectral bandwidth Δλ_m+n decreases with increasing diffraction order.

According to the specific geometrical conditions and grating properties of the demonstrator (see following section), Table 1 shows the maximum and the minimum detectable wavelength (λ_m+n,max and λ_m+n,min), and the respective spectral bandwidth Δλ_m+n in relation to the corresponding diffraction order.

Table 1. Maximum and the minimum detectable wavelength and the respective spectral bandwidth in relation to the corresponding diffraction order

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The longest wavelengths of the near infra-red region from 1030 nm to 858 nm are imaged in the 5^th diffraction onto the detector array. In the 6^th diffraction order the spectral interval from 858 nm to 736 nm follows. At the short wavelengths limit of the deep blue spectral range, the 12^th diffraction order covers the interval from 429 nm to 396 nm. Table 1 displays the decreasing spectral bandwidth Δλ_m with an increase of the detected diffraction order and decreasing wavelength.

 

Fig. 3. Multi-order concept: With increasing diffraction orders the single intervals ∆λ_m+n are expanded and experience a linear shift to larger diffraction angles.

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The previous discussion illustrates the requirements to fulfil the continuous condition at the transition from one diffraction order to the following. Additionally, with increasing diffraction orders and switching from one spectral interval to the next, the total spectrum as a combination of the single intervals Δλ_m+n is expanded and experiences a linear shift to larger diffraction angles (see schematics in Fig. 3). Both contrary tendencies, the reduction of the spectral bandwidth of each partial interval due to the continuous condition and the lateral stretching of each interval with increasing diffraction order are dominated by the first effect.

That means the total active area of the detection array with all pixels is addressed only by the interval related to the minimum diffraction order or equivalently at the limit of the long wavelength range. With increasing diffraction order and decreasing wavelength the number of pixels necessary to detect the particular interval is decreasing - the rest of the pixels are unused. This effect is expressed in Table 1 as the reduction of the enclosed diffraction angle Δ°_m with increasing diffraction order. In principal, the remaining pixels could also be used to detect the spectral information of the region which is attached to the short wavelength end of the interval of the particular diffraction order (m+n). On the other hand, this approach would lead to the disadvantage that the attained additional spectral information of the short wavelength range will also occur as a superposition in the next higher diffraction order (m+n+1) in the long wavelength regime of the (m+n) diffraction order. Finally it has to be mentioned that the angle resolution Δ°_m/Δλ_m (or pixel resolution) is increasing with decreasing wavelength.

3. Realizing the diffraction grating by interference lithography

Taking the diverse technological aspects for our purpose into account we found holographic Interference-Lithography (IL) to be the most suitable method for the mastering process of the imaging spectroscopic gratings. A fundamental advantage of correctly fabricated holographic gratings is that they are free of both the small periodic and the random groove placement errors which results in minimized disturbing stray light effects [6].

Additionally, IL allows to generate diffractive optical elements (DOE) with high diffraction efficiency and high spatial frequency over an extended field in a single exposure step on both plane and curved substrates.

In the basic IL process, a photo-resist coated substrate is exposed with a stationary interference fringe pattern generated by coherent beams. During the recording, a latent structure is created in the resist which is transformed into a continuous surface profile in the subsequent development process. To guarantee holographic gratings of high quality, precision optical elements with nearly diffraction-limited quality are necessary for the illumination setup, which have to be adjusted precisely on a stable optical bench.

Due to the typical exposure times which may take from minutes to hours, an extremely stable fringe pattern is required during the illumination process. Therefore an active control unit was introduced which allows to balance the optical paths of the interfering beams by the use of shifting piezo elements.

For the recording process of a concave grating two point sources (C and D) are required. In our exposure set-up the positions of the two point sources were determined by the distances $r_c\left(\overline{\mathrm{OC}}\right)=9.28\mathrm{mm}$ and $r_d\left(\overline{\mathrm{OD}}\right)=9.37\mathrm{mm}$ and the angles γ = 26.86° and δ = 18.33° between the central rays OC and OD and the grating normal (see Fig. 4). The asymmetrical recording geometry is required to minimize aberrations over the addressed spectral regions and causes varying groove spacing ranging from 3.2 μm to 4 μm over the grating diameter of 5 mm.

 

Fig. 4. Geometric positions of the point sources with respect to the substrate to record the miniature concave grating. The distance between the point sources C and D is 0.88 mm.

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A basic challenge of the recording process was to realize the two point sources C and D with nearly diffraction limited quality in close proximity to each other. With respect to the application set-up the recording configuration requires similar dimensions in distances and geometric relations. In our recording set-up, a distance of CD = 0.9 mm between the coherent point sources is required, whereas simultaneously a numerical aperture NA > 0.2 is necessary. A well established method to generate the origin of a single high quality spherical wave-front is to use a plane wave-front entering a collimating lens system with extended diameter and volume. Following this concept, the conventional approach to create two point sources employs two separated sets of collimating optics.

When the lateral distance between the two point sources has to be small the approach with the separated collimating optics is not suitable due to volume interference of the optical components. Especially in our configuration the required angle between the chief rays of both calculated ray bundles is too small to generate the point sources from separated optics sets.

In our recording set-up we applied a different concept to provide the two point sources in close proximity by using two wave-fronts entering a single set of collimating optics. Hereby a first plane wave is oriented perpendicular to the optical axis of the collimating optics whereas the second wave-front shows a slightly tilted angle with respect to the first plane wave.

Here it is essential to notice that in practice, the collimating optics used for interference lithography are optimized only for very small optical fields. In a reversed view that means that a plane wave tilted with respect to the optical axis of the recording optics will generate an imperfect, aberration affected focus. If this imperfect point source is used for the holography process the aberrations are transferred into the recording plane and cause a disturbed interference pattern. To illustrate this effect for our collimating optics set we calculated a decrease in the Strehl ratio from an on-axis value of 99.5 % to 17 % for the corresponding off-axis field position. It has to be mentioned that the limited optical field of the collimating optics optimized for IL is a result of the demand for high optical quality and simultaneously the necessity to minimize the number of optical surfaces which is indispensable to reduce the contribution of additional disturbing reflections. Especially our lens system offers a focus length of f = 92.7 mm and a usable diameter of approximately 50 mm.

The basic idea of our recording set-up was to neutralize the aberration induced by the tilted illumination of the collimating optics by the introduction of a supplementary hologram in the final recording configuration. The supplementary hologram itself is recorded in a previous process which in essential shows the reversed geometry related to the final assembly. Here, a near-perfect point source is located at the off-axis position of the calculated second point source. The propagating spherical wave passes the collimating optics and generates an outgoing wave-front on the back side which deviates from a perfect plane wave and shows the corresponding tilt angle. This unique wave-front is brought to interference with a plane reference wave-front and the resulting interference pattern is recorded on a plane, photoresist coated substrate (see Fig. 5).

 

Fig. 5. Recording of a supplementary hologram. The supplementary hologram is used to neutralize the aberration induced by the tilted illumination of the collimating optics.

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Fig. 6. Recording configuration for the concave grating. The supplementary hologram acts in the 0^th diffraction order as a plane mirror and generates a diffraction limited spot at the on- axis position. In the 1^st diffraction order the supplementary hologram generates a distorted wave-front which results in a second diffraction limited spot at the required off-axis position.

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After the development and the fixation of the interference pattern, the hologram is reintegrated and adjusted in the final recording set-up. The illumination of the supplementary hologram by the reference wave now allows in first order diffraction the reconstruction of the initial wave-front characteristics. After passing the collimating optics a diffraction limited spot is generated at the desired off-axis position.

In the final recording set-up a second plane wave-front, coherent to the reference wave-front, heads from a different direction to the hologram (see Fig. 6.). The orientation of this second wave-front is adjusted so that the plane substrate of the hologram acts as a perfect plane mirror (0^th diffraction order) and the corresponding part of the wave-front is reflected parallel to the optical axis of the collimating optics set. After transmission a second diffraction limited spot is generated at the on-axis position.

It is essential to notice that for both plane wave-fronts entering the recording system different diffraction orders have to be regarded: the 1^st diffraction order is decisive for the reference wave-front and the 0^th diffraction order for the second plane wave respectively. All the other diffraction orders from both plane waves have to be captured by light traps to avoid disturbing effects in the final recording surface. After providing the two required point sources C and D, the resist coated concave substrate selected for the final grating was adjusted in the recording set-up.

In our particular lithography process the light source was an Ar-Ion Laser working at a wavelength of 457.9 nm and offering a power of approximately 500 mW. The output beam of the laser was divided by a beam splitter into two coherent sub-beams which where expanded, collimated and directed under different incidence angles to the supplementary hologram. To ensure a maximum contrast of the interference pattern in the recording area the light intensities of both point sources have to be balanced. Hereby the varying diffraction efficiencies of the supplementary hologram for both plane waves and the according diffraction order have to be taken into account.

As a light sensitive recording material we used a positive i-line photo-resist (AZ 1505). The recording time was in the range of half a minute. The topography of the structure (periods between 3.2 μm and 4 μm, profile height about 1.43 μm) is approximately described by a sine curve and due to the exposure setup slightly asymmetrical in shape. Referred to the employed order, we achieve a diffraction efficiency of about 40% of the whole incoming radiation.

In the subsequent development process the latent interference pattern is transferred into a permanent surface relief structure which has been aluminium coated to allow a high reflectivity under the application conditions.

4. Spectrometer assembly and preliminary results

To proof the multi-order concept and the functionality of the imaging grating the microspectrometer was assembled in a demonstrator set-up which is shown schematically in Fig. 7. The demonstrator allows the necessary flexibility to adjust the imaging grating with respect to the detector array and to the entrance aperture.

As a detector we choose a CMOS linear image sensor with 1024 pixels, a pixel pitch of 7.8 μm (pixel height 125 μm) and an overall active area length of 7.99 mm [8]. The detector shows a spectral response range from 400 nm up to 1 μm with a peak sensitivity wavelength at 700 nm.

The entrance aperture and the detector array of the microspectrometer are located on the same plane in an aligned arrangement. A multimode fibre with 600 μm core diameter and an numerical aperture NA = 0.22 was used to pick up the light from the sample and served as the input aperture for the spectrometer.

As a first test sample for the experimental verification of the working principal of the spectrometer we choose a scattering surface (white paper) which is illuminated by the defined wavelengths of two different laser sources: a frequency doubled NdYAG-laser working at 532 nm and a HeNe-laser at 543 nm. The scattered light was gathered by the multimode fibre which was placed in close proximity to the illuminated surface.

Figure 8 shows the measured intensity as a function of the pixel number. In our demonstration experiment the overall length of the active area of the image sensor exceeds the design length of the detector by a factor of 2.5. That means the identical spectral range is imaged to adjacent areas on the sensor array by successive diffraction orders, so that the characteristic spectral features are repeated several times. The measured spectrum shows the repetition of two distinct peaks. Each of the individual peaks is attributed to one of the two test laser wavelengths.

 

Fig. 7. Demonstration set-up: A multimode fiber was used to pick up the light from a scattering surface (white paper) which was illuminated by the defined wavelengths of two different laser sources (532 nm and 543 nm).

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Fig. 8. Measured intensity as a function of the pixel number. Due to the multi-order concept the oversized length of the detection array results in multiple appearance of the characteristic spectral lines (lines: 543nm of a HeNe-laser and 532nm of a Nd:YAG-laser).

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In our set-up, the specific spectral range which includes both reference peaks at 532 nm and 543 nm is imaged by the 9th diffraction order on the front part of the active area of the detector array. In this area, the knowledge of both reference wavelengths allows a direct correlation of the pixel number to the wavelength. To estimate the resolution of the instrument, the full width of half maximum (FWHM) of the signal peak was measured to be 2.3 nm at 532 nm.

The considered spectral range is imaged in the 10th diffraction order onto the adjacent part of the array and additionally in the 11th diffraction order the associated features could be found on the array for the third time. The imaging position for the relevant wavelength range in the 11th diffraction order is far out of the design range. That means, the spectral imaging is strongly affected by aberrations and the original twin peaks of both laser wavelengths are reduced to non-characteristic features.

The observed reduction of the measured intensity with increasing pixel number is affected by several reasons. Exemplary aspects are the changed incidence angle with respect to the detection array (deviation from perpendicular) or the occurrence of field curvature and therefore reducing the imaging properties of the set-up.

To demonstrate the applicability of the multi-order concept over a broad wavelength range a number of defined spectral lines between 440 nm and 1000 nm were used as an input for the microspectrometer. Here, to select the appropriate wavelength, the continuous spectrum of a candescent lamp was dispersed by a monochromator and the exit slit of the monochromator couples into the multimode fiber which transfers the light directly to the entrance of the microspectrometer.

 

Fig. 9. (a). – (c). Measured intensities as a function of the wavelength for the three spectral intervals. The pixel distance between the 10 nm separated lines is decreasing with increasing wavelength range and simultaneously the accessible spectral width of each interval is increasing.

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Spectral lines of the intervals 440 nm – 460 nm, 580 nm – 640 nm and 860 nm – 1000 nm were coupled successively into the microspectrometer. Figures 9(a)–9(c) shows the measured intensities as a function of the pixel number for the three intervals. As discussed in the section describing the conception of the spectrometer the accessible spectral width of each interval is increasing with the wavelength which is correlated to the reduction of the diffraction order. Simultaneously Figs. 9(a)–9(c) shows that the pixel distance between the 10 nm separated lines is decreasing with increasing wavelength range. That means the highest pixel resolution correlates to the minimum wavelength range.

 

Fig. 10. Measure of the resolving power of the spectrometer. Two adjacent wavelengths (550 nm and 552.5 nm) were successively detected. The curve of both added signals shows a clear minimum between the peaks.

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An alternative measure of the resolving power of the spectrometer is shown in Fig. 10. Here, two adjacent wavelengths (550 nm and 552.5 nm) were successively detected. The added signal of both curves shows a clear minimum between the peaks,

5. Conclusion / Final remarks

We demonstrated the concept of a miniature spectrometer based on multi-order approach. This microspectrometer allows the access to a broad spectrum ranging from the far blue visible to the near infrared region in successive intervals. The individual spectral intervals may be addressed by switching selected spectral filtering systems or by applying light sources with adapted spectral bandwidth (e.g. LEDs).

Additionally, we presented a method to manufacture a miniature imaging dispersion grating by using a supplementary hologram in an interference lithography set-up. Hereby, the essential advantage of the set-up is the possibility to generate a point source separation below 1 mm which is necessary for the recording process. This approach to manufacture miniature imaging gratings is not limited to the multi-order strategy but could also be transferred to various application demands and different spectrometer concepts.