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Performance criteria for the choice of compact spectrometers

The market growth of miniature and compact spectrometers has been a significant development in recent years, and more particularly in OEM applications. Miniaturisation, robustness, cost reductions, and improvements in the performance of array detectors have allowed the use of these sensors in many industrial applications. These spectrometers which operate from the Ultraviolet to the near infrared range of the spectrum are used in many applications such as:

  • Colour Measurement
  • Analytical Chemistry
  • Biomedical
  • Fluorescence
  • Raman
  • Elemental Analysis 

The choices made by optical engineers and designers on the layout of the spectrometer can have a significant impact on the performance and effectiveness of the instrument not to mention the cost of manufacture. In this paper we hope to offer some simple guidance on this process. The performance of spectrometers is judged by three criteria:

  • System resolution
  • Throughput
  • System limit of detection

These criteria are affected by the grating efficiency, system light collection capability, system stray light and design aberrations. We offer brief discussions on each of these criteria in this paper.

Grating Efficiency

Holographic gratings are available with three different groove profiles. Each of these profiles has different efficiency advantages. Figures 1, 2, and 3 show the sinusoidal, laminar and triangular groove profiles, respectively. The maximum theoretical average efficiency (of unpolarised light) of the sinusoidal grating profile is around 35%.

 

Laminar and triangular groove profiles are produced with an ion etching process that shapes and controls the groove profile. The laminar profile grating improves the efficiency, but the main advantage of this profile is the reduction in second order efficiency. The second order is reduced to as low as 0.4%.

The triangular groove profile has efficiency profiles similar to ruled gratings. Peak efficiencies of 50% to 70% are possible.

 

System Light Collection Capability

Concave aberration corrected grating instruments are defined by the grating. Concave gratings are described by their arm lengths and included angle. The grating is the sole optical element in this design. The system light collection is determined by the f-number (f/#) of the grating. The f-number is the ratio of the grating focal length divided by the grating diameter (clear aperture). A lower f/# indicates a greater ability to gather light.

Aberration correction allows higher light collection compared with standard commercial spectrometer designs. Concave grating spectrometer designs with f numbers of f/2 and faster (toward f/1.5) are common. By comparison, most retail instruments use plane grating designs and operate at f-numbers between f/3 and f/10.

 

Aberration correction allows a spectrometer to operate at low f-number because of the reduction in the effects of aberrations. Low f-number designs, possible with concave gratings, offer the advantage of increased light collection capability over plane grating designs. Light collection capability comparisons of instruments can be done by taking the ratio of the squares of the design f-numbers. To compare the collection ability of a f/5 plane grating design instrument and a f/2 concave grating design, calculate the ratio of 5² to 2², or 25 to 4.

The light collection of f/2 concave grating design is more than six times greater than the equivalent f/5 design. The system collection efficiency is optimised with concave gratings while providing a simple, cost-effective design. Additional mirrors and mirror mounts are not necessary in these designs, making them more robust and intrinsically providing a better signal to noise ratio.

System Stray Light

The process of manufacturing holographic gratings has many advantages compared with ruled gratings for stray light rejection. First, it provides a better periodicity of the grooves that can not be achieved with a ruled grating. Additionally, it makes the grating surface smoother than ruled gratings. Surface roughness is a significant source of grating generated stray light (see picture below). It is important to remember that everything scatters light. All gratings exhibit some amount of scattered light.

The inherently lower scatter of holographic gratings improves the system performance.

 

Concave grating designs have two additional design advantages, with respect to system stray light, over most commercial plane grating designs. First, grating scatter in Czerny Turner and Fastie Ebert designs is collected and focused, by the focusing mirror, toward the exit port. In concave grating designs the grating does not focus its own scattered light into the focal plane. Secondly, rediffracted light is minimised. Rediffracted light is light that is diffracted by the grating and redirected back to the grating a second time (unintentionally of course).

When other concave optics (collimating and focusing mirrors) are used in an instrument design it is more likely that light may be rediffracted. Careful design effort is necessary to prevent rediffracted light. Concave gratings are immune from this problem when working at f-numbers greater than f/2 with low groove density (< 600 gr/mm) gratings.

Aberration Correction

Aberration correction is the most important benefit of concave aberration corrected holographic gratings. To understand the benefit of aberration correction it is important to understand the main aberrations in spectrometer designs and their impact on system results.

Optical components can create errors in an image even if they are made of the best materials and have no defects. These aberrations can be grouped into several different categories: spherical aberration, coma, astigmatism, and field curvature. The effects of coma, spherical aberration, astigmatism and field curvature can cause degradation of the system’s performance. Some description is necessary for how these aberrations relate to the exit focal plane of a spectrometer.

 

Spherical Aberration (SA)

Spherical aberrations result from the fact that the focal points of light rays far from the optic axis of a spherical lens or mirror are different from the focal points of rays of the same wavelength passing near the centre.

A spherical mirror does not precisely focus a point to a point. As light rays move further away from the centre axis of a mirror, the focal point moves closer to the mirror. A zone of confusion is created in the image plane because of the changing focal point with distance from centre axis. This "zone" of confusion prevents the ability to obtain a sharp focused image. SA is difficult to eliminate without the use of aspheric optics.

The result of SA is loss of resolution. Imaging performance degrades causing crosstalk from adjacent wavelengths. In aberration corrected designs the concave grating is designed to correct SA.

Coma

Coma is an aberration resulting from using off axis optics. Coma causes an unsymmetrical spectral line broadening. This broadening leads to resolution losses and stray light. On a detector array, the impact is pixel to pixel crosstalk and loss of resolution.

Coma can be corrected in some instruments, at one wavelength, by adjusting the optical geometry. Coma can be corrected at many wavelengths in the concave aberration corrected grating design.

Astigmatism (AST)

Astigmatism (AST) is another aberration resulting from the use of off axis optics. Point sources "grow" in height as the longitudinal astigmatism increases. Longitudinal astigmatism is the result of the tangential and sagittal components focusing in different planes.

Astigmatism effects can lead to a 400 micron input fibre (at the input slit position) "growing" to 2 millimeters high at the output focal plane. When using a 0.5 millimeter high array, and the exit focal plane image is 2 millimeters, 75% of the output signal is not measured. This effect leads to loss of system throughput and the limit of detection.

Field Curvature (FC)

Field curvature (FC) is the shape of the image plane (usually called the Petzval Field). The shape of the field determines the shape of images at the exit. Field curvature can cause calibration errors for off-axis sources and pixel to pixel crosstalk on arrays. Calibration errors and increased blur of off-axis inputs are considered stray light. Aberration corrected gratings can change the shape of the exit focal plane field.

Aberration Conclusion Review

Coma, SA, and FC contribute to near end stray light (light from adjacent wavelengths). Light that does not properly strike the detector decreases the system performance. The signal to noise ratio suffers because of low throughput per pixel and increased pixel to pixel crosstalk.

Putting the advantages of efficiency, system light collection capability, system stray light advantages and aberration correction together provides a clear view of the advantages of the holographic concave aberration corrected grating designs. The performance advantages of aberration corrected concave gratings, together with the simple, compact and robust design optimise system performance.

Technology Pushing Instrument Design

In the past three decades detector technology has progressed from film to phototubes to photodiode arrays to charge coupled devices (CCDs). The use of small diameter optical fibres (with high numerical apertures) coupled with new detector technology has made improving imaging performance of existing instruments much more important.

Good off axis performance has become necessary as applications using fibre arrays and tall CCD arrays are used together in applications. It is in this area that aberration corrected holographic grating designs have made the biggest impact. Aberrations such as coma, spherical aberration, astigmatism and field curvature make point to point imaging a difficult challenge.

Commercially available instruments are designed as all-purpose instruments. They must adapt to applications that work well in the Ultraviolet through the far infrared in scanning and image modes. For dedicated industrial applications, a more specific design can lead to an instrument that outperforms the all-purpose, one size fits all, instrument design.

For those users with dedicated, repetitive applications (as with most OEM grating customers), spectrometers with concave gratings are the obvious choice. Another advantage of aberration correction gratings well worth mentioning is the ability to correct for aberrations in other parts of the optical system.

Other system aberrations (e.g., aberrations from lenses, mirrors or sample-related problems) can be corrected with an appropriate grating design. The concave aberration corrected grating design can incorporate the required corrections for system coma, spherical aberration, astigmatism and field curvature. This system design approach can improve resolution and spatial imaging.

Design success will often depend on achieving the optimal coupling of all system components. Aberration corrected holographic grating designs are used in many industrial systems to optimise throughput while reducing noise.

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