The modern imaging spectrograph has become the dispersive instrument of choice for spectral analysis in applications ranging from Raman spectroscopy to laser-induced breakdown spectroscopy. Most of the instruments used in these applications are research-grade spectrographs (RGSs).
From a design standpoint, the RGS is intended for use in the widest possible range of applications. To meet the requirements of such varied applications, engineers typically incorporate a balance of performance and versatility. In some instances, however, adding features and capabilities can lead to compromises in optical performance. As applications mature, there is often a migration from the research laboratory to commercial markets, necessitating the move from RGS systems to more specialized application-engineered imaging spectrographs (AEIS). Making the Grade
Figure 1. Analysis of minimum-attainable spot size with respect to off-axis angles and aperture ratio (/#) shows the increase in spot size with increasing angle.
All spectrographs are designed to disperse light into individual wavelength components and record this spectral information, nearly always with CCD detection systems. The engineering of modern RGSs focuses on preserving spatial image quality, which enables the user to incorporate multiple illumination fibers or sources while maintaining discrete information from each source. This approach enables a single imaging spectrograph to perform the work of several independent spectrographs.
To increase market potential, the RGS is usually designed to accept a wide range of commercial CCD detection systems, forcing system compatibility with a variety of mounting configurations and detector sizes. If designed for multiple entrance and exit ports, the RGS must accommodate mirrors that can swing in and out of position for port selection. Multiple-grating turrets allow two or more gratings to be mounted on a turret and rotated into position when needed. From a design consideration, this requires enough space to swing the turret when changing gratings.
All of these features add versatility but impact the physical size of the instrument, as well as the off-axis angles of internal mirrors. Flexibility introduces other, more important disadvantages. Increasing off-axis angles to accommodate large-area detectors, grating turrets, and moveable beam-diverter mirrors has a negative impact on the optical imaging performance of a spectrograph. For any given aperture ratio (/#), a direct correlation exists between the off-axis angle of a mirror and minimum-attainable spot size for the optical system (see figure 1). The analysis shows that increasing the off-axis angle by a factor of two essentially doubles the minimum spot size. Increasing the light-collection ability of the optical system by increasing the aperture ratio will also increase optical aberrations. These are both key factors to consider when designing the modern RGS. Engineering for the Application
Typically used by original equipment manufacturers (OEMs) and buried deep within commercial equipment, AEIS systems are designed and manufactured to meet a set of application-specific requirements. This level of specialization allows the engineer to design a compact, rugged optical system with high performance, few or no moving parts, and high reliability. Most AEIS systems begin as baseline RGS designs that provide the spectral resolution and spatial imaging performance required for the application. Use of the RGS allows the designer to explore a number of different parameters to fully optimize the system before moving from prototype to production systems.
The first step in the design process is to establish specifications for wavelength coverage, spatial imaging performance, and spectral resolution. In addition, an AEIS typically has to meet certain size limitations in order to fit into an OEM system. Consider an AEIS system for microscopy. In this case, a 40-nm near-IR spectral band has to be dispersed across a 6.5 mm x 6.5 mm CCD detector. The performance requirement for spatial imaging specifies that at least 50% of the light from a 10-µm-diameter pinhole image must focus on a single 13 µm x 13 µm pixel. Spectral resolution for this application has to be better than 2 nm and will be driven largely by dispersion and entrance-slit width.
To determine dispersion D, we use
D = (cos(φ + α) x 106)/(g f n)
where φ is grating angle of rotation (see figure 2), α is the half angle, g is the groove spacing, f is the focal length, and n is the grating order (usually 1). By selecting a focal length of approximately 240 mm and a grating groove density of 600 g/mm, we achieve a dispersion of approximately 6.9 nm/mm, satisfying the wavelength requirements of the application. Since this is a dedicated system, we can define a focal length to meet the specific spectral window requirement for the application. This particular application did not require order sorting, which can be an effective tool for single- channel applications (scanning) and multichannel systems.
Figure 2. Calculations of dispersion require knowledge of the grating angle of rotation φ and the grating half angle α.
Spatial imaging performance is also important to the success of the application. The design objective was to image 50% of the light emitted from the 10-µm-diameter point source through the optical system and onto an individual 13 µm x 13 µm detector pixel. In contrast, a typical RGS design images the same 10-µm-diameter source as a 35- to 100-µm spot, depending on the focal length and aperture ratio of the system. Achieving the desired imaging performance requires tight control and optimization of the optical system.
Typical aberrations that can impact imaging performance include astigmatism, chromatic aberration, and spherical aberration. Astigmatism is introduced when spherical mirrors are used at an angle other than normal incidence, causing a displacement of the tangential and sagittal focal planes. We can correct for this type of aberration by using a toroid in place of the collimating mirror. The toroid adds additional optical power in the vertical direction to bring the two focal planes together. This type of correction is common for both RGS and AEIS systems. Fortunately, there is no chromatic aberration in mirror-based systems, so this is not an issue for either spectrograph.
Spherical aberration plays an important role in the ultimate image quality attainable by a system. Factors that can be controlled to improve image quality include off-axis angles and the aperture ratio of the AEIS optical system. In our example, we are required to match the aperture ratio of a specific light collection lens assembly; figure 1 clearly demonstrates that we must minimize off-axis angles to meet the required imaging performance. Fundamental limits to angle reduction are usually physical in nature. We must take into account the physical size of the optics and the specific CCD detector, and design the system such that all desired optical rays pass through the system unobstructed. If we keep the off-axis angles to approximately 6° or less and choose an aperture ratio of approximately /12, we can achieve the desired imaging performance of 13 µm.
Tests show that the system as built achieves the required spatial imaging performance (see figure 3). With imaging performance optimized, the final step in the design process is to optimize light throughput over the desired spectral region for the application.
The Coating Factor
Figure 3. The corrected design images the required 50% of the light on a pixel of the CCD detector. Each square on the grid corresponds to a 13 µm x 13 µm pixel.
One of the most overlooked areas of potential improvement to spectrograph performance is in the area of optical coatings. RGS mirrors are typically coated with aluminum and magnesium fluoride (Al+MgF2) because it is relatively inexpensive and offers broadband reflectance of about 84 to 90% over the UV to near-IR spectral region. In systems with several mirrors however, 10 to 16% loss per reflection can significantly reduce throughput, negatively impacting the signal-to-noise ratio and ultimately the detection limits of the system.
Advanced optical coatings are designed for near total reflection over a pre-defined spectral region, offering the potential to significantly improve system throughput. Coatings consisting of many thin layers of alternating high and low index materials can achieve near total reflection over a desired spectral window. Reflection at wavelengths away from the primary spectral window typically remains on the order of 5 to 10% and can be further optimized by varying the layer thicknesses. Near total reflection increases system throughput while low reflection away from the primary spectral window reduces potential stray light levels. In principle, these thin-film stacks can be manufactured for improved performance at UV, visible, or near-IR wavelengths.
In tests, the use of advanced optical coatings resulted in a 40% increase in system throughput over the 40 nm spectral width compared to conventional optics. Those same tests showed that the coatings reduced unwanted out-of-band light by a factor of four or more. Other advantages of specialized coatings can include low absorption for resistance to laser-induced damage and high durability to minimize damage in severe environmental conditions.
Although the advantages of increased system throughput and lower stray light are highly desirable, costs may may be somewhat prohibitive for the individual user. Specialized coatings will typically be more expensive than conventional coatings and there may be non-recurring engineering charges. In most cases, the application of specialized coatings will be desirable for OEM applications involving dedicated use, for which multiple systems using the same type of coatings can be manufactured.
With proper design, an engineer can tailor the benefits of the RGS to the application at hand, achieving cost, size, and performance efficiencies. In this case, the AEIS system provides near-pixel-limited imaging capabilities over a focal plane height of 6.5 mm, with improved throughput from coating optimization. Clearly, the merging of optical design with coating technologies offers potential for significant improvements to system imaging performance, throughput, and stray-light rejection. oe
Michael Case is vice president of R&D at Acton Research Corp., Acton, MA.