Introduction to the operating principles of the HyperFine
spectrometer
LightMachinery Inc., 80 Colonnade Road North, Ottawa ON CanadaA spectrometer is an optical instrument designed tosplit light into separate colors, or wavelengths.
Thus, white light directed into a spectrometer will
be separated into red, green, yellow, and blue lightat the exit of the spectrometer.
Inside a spectrometer, a variety of opticalcomponents can be used to separate thewavelengths. The choice of component depends
primarily on the required resolving power, R (1). Aglass prism is sometimes used for low-resolution (R<1000) instruments, but the most common opticalcomponent used in modern spectrometers is adiffraction grating (2). Diffraction gratings are usedin either transmission or reflection, and generally
provide resolving powers in the range of 1000 to
100,000. However, to use diffraction gratings at
higher resolutions, requires the use of increasingly
larger gratings.
To illuminate large diffraction gratings, optics withlarge diameters and long focal lengths (large fnumbers)(3) are required to minimize aberrations. A
large entrance focal length (together with a narrowslit) is also required to achieve high resolution due
to imaging considerations. Hence, diffraction
grating instruments with R > 50,000 are generallyexpensive (>$50,000) and large (>1 meter inlength).
For high-resolution spectrometers, Fabry-Perot (FP) etalons provide a compact and cost-effective
method to separate closely-spaced wavelengths.
Figure 1 explains the principle of the F-P
interferometer (4).

Note that the condition for transmission of aparticular wavelength, , is that a round-trip
between the etalon plates must be exactly an
integral number (m) of wavelengths. If the plate
separation, d, is 0.25 mm, then a round trip is equal
to 1,000 at 500 nm, and it is easy to show (4) that
it is possible to achieve R ~50,000 with a highquality etalon with a 0.25 mm plate separation using
sufficiently reflective coatings.
While F-P etalons provide high resolution, they
suffer two significant drawbacks. Firstly, only asmall fraction of the incident wavelength istransmitted through the etalon; the majority of theincident light is reflected and lost to themeasurement system. Typically, >95% of the lightincident on the F-P etalon is wasted. The second
drawback with a F-P etalon is the problem ofoverlapping orders. In the example above, light ofwavelength 500 nm is transmitted through the 0.25mm etalon because exactly 1000 wavelengths fit
into a round-trip in the etalon. However, light with awavelength of 500.5 nm will also be transmitted
through the etalon, this time with exactly 999
wavelengths in a round-trip. The measurement
system cannot distinguish between these two
wavelengths, which are termed overlapping orders(order #999 and #1000, in this case).
A special type of etalon, called a VIPA (VirtuallyImaged Phased-Array), can be used in combination
with a grating to overcome the two drawbacks ofthe Fabry-Perot etalon, while still retaining its highresolution. The HyperFine Series of spectrometers
is based on LightMachinery’s patented VIPA (6)technology. Figure 2 shows the principle ofoperation of a VIPA.

Figure 1: Principle of operation of an F-P interferometer(5).
1Figure 2: Principle of operation of a VIPA, which
consists of two parallel reflecting surfaces (one ~100%
reflective, one ~95% reflective). A cylindrical lens isused to focus the light into the VIPA through an antireflection coated slot in the R = 100% coating (7).

Once light is focused into the tilted VIPA, it can
only exit in the forward direction – through the 95%
R surface (the 100% R surface does not allow any
light to be reflected backwards). Hence, in principle,
the VIPA allows all the incident light coupled into
the VIPA to be imaged into the measurement
system – a significant advantage over a
conventional F-P etalon that typically reflects andwastes over 95% of the incident light.
In other respects, VIPAs and F-P etalons behave ina similar fashion, as illustrated in Figure 3.

Figure 3: Typical light patterns for FP-etalons andVIPAs illuminated by a single wavelength of light. On
the left is the pattern of light transmitted by an F-P etalon
illuminated by the cone of light from a spherical lens. On
the right is the light pattern transmitted by a VIPA
illuminated by the same source and focused by acylindrical lens.

In many respects, the light pattern transmitted by a
VIPA is equivalent to a thin “slice” of the lightpattern transmitted by the F-P etalon. Hence, aspectrometer based on a VIPA still faces the issueof overlapping orders as illustrated in Figure 4.

Figure 4: Three adjacent orders transmitted by a VIPA
as the wavelength of the incident light is tuned in steps
from 550.00 nm to 550.06 nm. Note that the VIPA
cannot distinguish between light at 550.00 nm and550.06 nm. The separation of these two wavelengths,
0.06 nm or 60 pm, is termed the Free Spectral Range(FSR) of the VIPA, and corresponds to a glass VIPA
with a thickness of 1.68 mm (6).

Fortunately, for a VIPA illuminated using acylindrical lens as shown in in Figure 2, the various
orders and wavelengths are dispersed (8) only in thevertical direction (unlike the F-P etalon, asillustrated in Figure 3). Hence, adding a crossdispersing element that provides dispersion in thehorizontal direction can separate the overlappingorders. The resolution in the horizontal directionneeds only be sufficient to separate the adjacentorders. In the HyperFine spectrometer, the crossdispersion is provided by a reflective diffraction
grating, as illustrated in Figure 5.

Figure 5: Schematic layout of the optical components in
a HyperFine spectrometer (9). The VIPA disperses theincident light in the vertical direction, providing a highresolution, but also overlapping orders. The grating
separates the overlapping orders in the horizontaldirection.

With the VIPA and grating providing dispersion in
the vertical and horizontal directions respectively, alens assembly can be used to focus all the different
wavelengths onto the surface of a CMOS camera.
The lens converts angles (in vertical and horizontaldirections) into position on the CMOS array at the2

focus of the lens. Figure 6 illustrates the crossdispersed spectrum as seen by the camera.

Figure 6: Schematic of the display expected at theCMOS camera when the crossed VIPA and grating are
illuminated with broadband (“white”) light. In thevertical direction, the VIPA provides high resolution, but
only for a range of one FSR. In the horizontal direction,
the grating separates the overlapping orders to allow theentire high-resolution spectrum to be “unwrapped”. Thus,
the vertical stripes are spaced by one FSR in thehorizontal direction. In the chart, red represents longer
wavelengths; blue shorter wavelengths. A typical screen
shot from the camera is shown on the right. Only a small
portion of the full CMOS sensor is shown, covering 23
FSRs of the VIPA horizontally, and 0.5 FSR vertically.

The LightMachinery HyperFine spectrometer
combines high resolution (provided by the VIPA)
with an extended measurement range (provided bythe grating) (10), and utilizes modern megapixel
camera arrays together with custom software toprovide unprecedented performance from aspectrometer of modest size and cost.

Recording and calibrating spectra with
the HyperFine Spectrometer
Each HyperFine spectrometer ships with custom
software that allows the user extensive control overthe display, recording, and calibration of the spectra.
At the most elementary level, the user has access to
the raw output from the CMOS sensor, and canwrite their own software to analyze specific spectral
records. Figure 7 shows examples of the raw sensor
display for both broadband light and a
monochromatic light source.

Figure 7: Typical CMOS sensor displays when theHyperFine spectrometer is illuminated with broadband
light (upper), and a narrow-line-width monochromatic
laser (lower). The full spectrum can be extracted by“unwrapping” the information in the regions marked witha box.

Figure 7(upper) is the same image as Figure 6, only
zoomed out slightly. In the horizontal direction, the“stripes” of light are separated by one FSR of theVIPA. Figure 7(lower) shows 3 separate intense
spots of light in the vertical direction. Each spot
represents a separate VIPA order, but each spot isformed by light of exactly the same wavelength (thewavelength of the monochromatic laser)(11). Thus,
there is generally redundant spectral information in
the vertical direction as the spectral features repeat
in each spectral order. The full spectra can beextracted by “unwrapping” the information
contained in the sensor region indicated by theboxes in Figure 7. The HyperFine software takes theinformation from images similar to Figure 7 andcalibrates the entire CMOS sensor in bothhorizontal and vertical directions in units of theVIPA FSR. The software then determines the rangeof “useful” pixels, and the procedure to be used in
the “unwrapping” process.
In principle, if both the wavelength of the laser used
to record Figure 7(lower), and the exact FSR of theVIPA are known, the “unwrapped” spectrum can becalibrated in absolute wavelength. However, ingeneral, it is more accurate to input a second known
wavelength into the HyperFine spectrometer, and touse the positions of the two known wavelengths tocalibrate the entire spectrum. The HyperFine
3

software can utilize either approach, resulting in aspectrum that is calibrated to better than 5 pm overthe entire wavelength range.
Sunlight is an ideal light source for demonstrating
the performance of the HyperFine spectrometer.
Sunlight is the original “white light” source, is
inexpensive, and provides intense blackbody
radiation from the UV to the IR. More than 40,000
discrete absorption lines (Fraunhofer lines) (12) aresuperimposed on the black-body background, andseveral of these lines have line widths of less than
10 pm (13). The Fraunhofer lines are distributed
throughout the wavelength region from 270 nm to1600 nm, and the spectral positions of the vast
majority of the lines are accurately known. Figure 8
shows two raw CMOS images taken by dispersing
sunlight in the HyperFine spectrometer.

Figure 8: CMOS sensor images of sunlight taken with aHyperFine spectrometer. (The upper image covers theregion from 527 to 547 nm, while the lower image covers
a smaller spectral region from 532 541 nm). Multiple
dark regions – each of which represents a Fraunhofer
absorption line, interrupt the white light background of
the sunlight. The red box in each image indicates one
VIPA FSR in the vertical direction. The images wereoverexposed (i.e. highly saturated) for increased
visibility.

Figure 9: The upper trace shows the output from theHyperFine software once it has analyzed images such as
those shown in Figure 8. The labels in red are the ionicspecies responsible for the individual absorption lines inthe solar background, and the labels were added once theHyperFine spectrum was compared with a spectrum fromthe literature (14).

Figures 8 and 9 illustrate the performance of theHyperFine spectrometer when it is illuminated withbroadband light containing many spectral features.
At the other extreme, many applications involve theinvestigation of light sources that are almost
monochromatic, but require extremely highresolution (Brillouin and Raman spectroscopy,measurement of diode laser modes, etc.). To
demonstrate the performance of the HyperFine
spectrometer with this type of light source, the input
to the HyperFine spectrometer was illuminated withthe output of a green He-Ne laser. This laser
operates near 544 nm, and the narrow line-width of
the gain medium is expected to support two or threelongitudinal modes with a spacing of only 0.5 pm(corresponding to a 30-cm long laser). Figure 10
shows the raw CMOS image, and the extracted
spectrum.

The HyperFine software takes these images,
unwraps the spectrum, calibrates the wavelengthscale and produces output such as that shown inFigure 9.

4

instruments, and additional examples of measured
spectra can be found in companion documents (15).

References and footnotes
1) If two wavelengths , and +, can just beseparated (or resolved) by a spectrometer, theresolving power of the spectrometer, R is definedby:
R = /Hence, a spectrometer operating at 500 nm with R =10,000 can just separate two wavelengths that are
spaced by 0.05 nm or 50 pm.
2) The link below provides a description ofdiffraction gratings:
https://lightmachinery.com/optical-designcenter/library/users-guides/grating-designer-usersguide/A calculator for diffraction gratings can be found at:https://lightmachinery.com/optical-designcenter/more-optical-design-tools/gratingspectrometer-designer/

Figure 10: CMOS sensor image recorded when the lightfrom a green He-Ne laser was input to the HyperFine
spectrometer (upper). Four different VIPA orders arerecorded in the vertical direction (The VIPA is 5 mm
thick with an FSR of 20 pm). Each order shows thedistinct mode structure of the He-Ne laser. The extracted
spectrum displayed in (lower) shows that thespectrometer can resolve the longitudinal laser modes
which are separated by only 0.5 pm (500 MHz or 0.17cm-1).

It is worth pointing out that the spectral resolution
demonstrated in Figure 10 is equivalent to a
resolving power of ~0.5 pm at a wavelength of 500
nm, or R = one million. Spectrometers with aresolving power this high are generally very large(>2 meters) and very expensive instruments(>$100,000).

Additional information
This document is meant to provide an introduction
to the principles of operation (and the softwareimplementation) of the new line of LightMachinery
high-resolution spectrometers. More detailed
information on the operation of the spectrometers
can be found in the manuals provided with the3) The f-number of an optical system such as a lensis the ratio of the system's focal length to thediameter of the entrance pupil. It is a dimensionless
number that is a quantitative measure of lens speed,and an important concept in photography andspectrometer design.
4) The link below provides an introduction to
Fabry-Perot etalons:
https://en.wikipedia.org/wiki/Fabry–
Pérot_interferometer
A calculator for F-P etalons can be found at the link
below:
https://lightmachinery.com/optical-designcenter/etalon-designer/
5) Reprinted from:http://hyperphysics.phyastr.gsu.edu/hbase/phyopt/fabry.html
6) A detailed description of VIPAs can be found at
the link below:
https://lightmachinery.com/optical-designcenter/library/users-guides/vipa-designer-usersguide/5

A VIPA calculator can be found at the following
link:
https://lightmachinery.com/optical-designcenter/more-optical-design-tools/vipa-designer/
7) Reprinted from:
Metz, Philipp, et al. Optics express 21.3 (2013):
3324-3335
8) Prisms, gratings, and etalons all separate theincident light into its components by ensuring thatdifferent wavelengths emerge at different angles –this variation in angle with wavelength is called
dispersion.
9) Reprinted from:
Van den Berg, Steven A., et al. Scientific reports 5(2015): 14661.

13) Line-widths of a few of the stronger Fraunhoferlines are listed at: http://www.coseti.org/9006025.htm
14) Beckers, Jacques M., Charles A. Bridges, andLou B. Gilliam. A High Resolution Spectral Atlasof the Solar Irradiance from 380 to 700 Nanometers.
Volume 2. Graphical Form. No. AFGL-TR-76-0126(II). AIR FORCE GEOPHYSICS LAB HANSCOM
AFB MA, 1976.
15) Additional documents available from
LightMachinery describe high-resolution spectra ofHg calibration lamps, solar radiation, picosecond
lasers, and Brillouin scattering

10) The crossed-dispersion feature of the HF
spectrometer is similar to that used in spectrometers
based on echelle gratings. However, echelle-grating
instruments with resolving powers comparable to
the HF spectrometer are generally much larger andmore expensive.
11) Each VIPA order is centered on a different“stripe”, as shown schematically below:

12) An introduction to the Fraunhofer lines can befound in the Wikipedia article:
https://en.wikipedia.org/wiki/Fraunhofer_lines
A more detailed description of the solar spectrum isgiven in a NASA presentation:
http://mark4sun.jpl.nasa.gov/report/UT_seminar_So
lar_Spectrum_Toon.pdf

6