Compact diffraction grating laser wavemeter with sub-picometer accuracy and picowatt
sensitivity using a webcam imaging sensor
James D. White and Robert E. Scholten
Citation: Review of Scientific Instruments 83, 113104 (2012); doi: 10.1063/1.4765744
View online: http://dx.doi.org/10.1063/1.4765744
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REVIEW OF SCIENTIFIC INSTRUMENTS 83, 113104 (2012)
Compact diffraction grating laser wavemeter with sub-picometer accuracy
and picowatt sensitivity using a webcam imaging sensor
James D. Whitea) and Robert E. Scholtenb)
ARC Centre of Excellence for Coherent X-ray Science, School of Physics, The University of Melbourne,
3010 Victoria, Australia
(Received 7 June 2012; accepted 21 October 2012; published online 27 November 2012)
We describe a compact laser wavelength measuring instrument based on a small diffraction grating
and a consumer-grade webcam. With just 1 pW of optical power, the instrument achieves absolute
accuracy of 0.7 pm, sufficient to resolve individual hyperfine transitions of the rubidium absorption
spectrum. Unlike interferometric wavemeters, the instrument clearly reveals multimode laser operation, making it particularly suitable for use with external cavity diode lasers and atom cooling and
trapping experiments. © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4765744]
I. INTRODUCTION
The use of tunable lasers, in particular extended-cavity
diode lasers (ECDLs),1–4 has become ubiquitous in atom optics. Knowledge of the wavelength is critical, for example, so
that the laser can be tuned to an atomic transition of interest. The spectral width of atomic transitions is typically 106
times smaller than the tuning range of the laser, and to find
the Doppler-broadened line in a vapor reference cell requires
wavelength measurement with picometer (1 part in 106 ) absolute accuracy. Wavemeters with the necessary precision and
accuracy are readily available commercially, but they are expensive and often excessive when the required measurement
range is only a few nanometers. There are also many excellent
descriptions of self-constructed interferometers with resolution of 106 –1011 ,5–11 but they can be large and complex. Twocolor photodiodes have not achieved accuracy better than
25 pm.12, 13 Moreover, all of these devices are prone to error if the laser is operating in multiple longitudinal modes, a
common problem with ECDLs.
Grating spectrometers are low in cost, reliable, readily
available commercially, and simple enough to construct in the
lab, but they are generally considered to have insufficient resolution, typically no better than 50 pm (25 GHz). Here we
reconsider the grating spectrometer for high resolution measurement, although over a relatively narrow spectral range.
Grating spectrometers are usually designed for broad spectral range, linear dispersion, high optical efficiency, and high
optical resolution so that adjacent wavelengths can be distinguished. For measurement of a laser wavelength, these characteristics are less important. The tuning range of an ECDL
is typically no more than 10 nm and linear dispersion is of
little value when the light source is at one frequency only.
The extremely high sensitivity of semiconductor imaging sensors means that high optical efficiency is not needed for bright
laser sources. With a laser, there is no need to resolve closely
spaced lines and thus we can accept a relatively wide wave-
a) Permanent address: Juniata College, Huntingdon, Pennsylvania 16652,
USA.
b) Electronic mail: scholten@unimelb.edu.au.
0034-6748/2012/83(11)/113104/4/$30.00
length resolution and use computer interpolation to find the
line center.
This report describes a simple grating-based spectrometer with an off-the-shelf consumer HD (high definition)
“webcam” imaging sensor, a small (15 mm × 15 mm) reflective diffraction grating, one or two lenses, and a single mode
fiber. The usefulness of webcams in grating spectrometers has
been described elsewhere with emphasis on their application
to undergraduate laboratory projects;14, 15 here we emphasize
the application for laser wavelength measurement. The absolute accuracy is ±0.7 pm (1 standard deviation) with correction for the measured air temperature and pressure, corresponding to 350 MHz, which is smaller than the Doppler
broadened width of a single hyperfine transition in roomtemperature rubidium vapor. The CMOS webcam sensor has
very high sensitivity: the optical power required to saturate
the sensor at a frame rate of 10 Hz is only 1 pW. Accurate
measurements can be obtained with a bare single-mode fiber
placed in a 10 nW laser beam without input collimation lens.
The fiber core also forms a very small “slit” for high resolution imaging in the spectrometer.
II. DESIGN
The design is shown schematically in Fig. 1. Light from
the single-mode fiber expands and is collimated by lens f1 before striking an 1800 line/mm planar reflective holographic
grating.16 The diffracted beam passes through a second lens
f2 that reimages the fiber core onto the bare camera sensor16
(lens and IR filter removed). Achromatic doublet lenses were
used because they provide higher resolution, particularly offaxis, in comparison to spherical singlets.
We used 25 mm diameter lenses and a 15 mm × 15 mm
diffraction grating to create a compact device. The first lens
focal length f1 was chosen to fill the grating. The beam divergence from the fiber is sin−1 (NA), where NA = 0.12 is
the numerical aperture of the fiber, and hence the beam diameter is 15 mm at a distance of 65 mm. The lens focal length f1 should then be longer than 65 mm; we used
f1 = 120 mm. The second lens determines the image magnification and hence the wavelength range and resolution. For
83, 113104-1
© 2012 American Institute of Physics
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113104-2
J. D. White and R. E. Scholten
Rev. Sci. Instrum. 83, 113104 (2012)
x
webcam
1920x1080
f2
grating
Relative intensity
1
778.15
single-mode fiber
0
776
θ2
θ1
FIG. 1. Schematic representation of the wavemeter. Doublet lens focal
lengths f1 = 120 mm, f2 = 200 mm; grating 1800 line/mm planar reflective holographic; θ 1, 2 = 30◦ , 65◦ ; and webcam CMOS sensor, 1920
× 1080 pixels each 3μm square (lens and IR filter removed).
f2 = 200 mm and sensor width of 6.0 mm, the practical
wavelength range was about 6.7 nm. A single-lens configuration with grating angle in near-Littrow configuration (θ 1
∼ θ 2 ) was also successful.
For a sinusoidal holographic grating, the diffraction angle
is given by the grating equation
λ
(1)
d
for wavelength λ, where θ 1, 2 are the incident and output angles and d is the grating pitch. The displacement at the sensor
is x = −f2 θ 2 and the dispersion is
2 −1/2
dx
f2
λ
=
− sin θ1
,
(2)
1−
dλ
d
d
sin θ1 + sin θ2 =
which is approximately 8.4 × 105 for the configuration in
Fig. 1 (θ 1 = 30◦ , θ 2 = 65◦ ). That is, at λ = 780 nm, a wavelength change of 3.5 pm will shift the image by one pixel on
the sensor (3 μm).
The wavelength resolution of the spectrometer is determined by a convolution of the effective slit aperture
size, the grating dispersion, and the imaging resolution. The
minimum size of the image of the fiber core, assuming
diffraction limited lenses and specular reflection, is wsensor
= (f2 /f1 )wcore = 8.3 μm (1/e2 ), equivalent to 3.5 μm fullwidth at half maximum (FWHM). This width is small compared to the width of the grating diffraction function,17 approximately dλ = λ/N where N is the number of grating rulings illuminated (15 × 1800 = 27 000); i.e., dλ
= 0.03 nm, corresponding to 8 pixels = 25 μm full width or
11 μm FWHM at the imaging sensor. The measured width
(see Fig. 2) was 21 μm FWHM, corresponding to a wavelength resolution of 24 pm.
The resolution of a spectrometer is usually defined in
terms of this spectral width, but laser linewidths are typically
much smaller than the spectrometer linewidth. When using
the device as a wavemeter we can interpolate the diffracted
image to find the center with much greater precision than defined by its spectral width, and as shown in our results, the
resolution can be improved by a factor of 30.
778
779
Wavelength
780
778.25
781
782
λ (nm)
FIG. 2. Sample of spectrum. Inset shows expanded region near laser line,
with Gaussian fit (solid line).
III. CALIBRATION
Spectra were acquired using the videoinput function
of MATLAB. Each image was converted to grayscale and averaged over several image rows; an example of an acquired
spectrum is shown in Fig. 2. The peak center was found by fitting to a Gaussian function. The spectrometer was calibrated
using a tunable laser at a series of wavelengths spanning the
extent of the imaging sensor, while simultaneously measuring
the wavelength with a commercial wavemeter16 (absolute accuracy ±0.1 pm); see Fig. 3. Up to 100 measurements were
averaged at each wavelength.
The wavelength is related to the pixel location by Eq. (1),
which is linear to one part in 107 over the limited wavelength
range. Spherical aberration caused deviation from the linear
relationship by up to ±0.01 nm. A second-order polynomial
fit to the calibration data improved accuracy by a factor of 30;
the calibrated wavelength was then accurate to ±0.7 pm.
If a high-precision wavemeter is not available, the spectrometer can be calibrated with reference to known transitions
as described in a later section.
The absolute value of the wavelength measurement depends on structural stability and environmental variables including temperature, pressure, and relative humidity (RH).
Calibration consistency from day to day requires solid
783
Wavelength (nm)
f1
777
778.2
782
781
780
779
778
200
400
600
800
1000
1200
Pixel
FIG. 3. Calibration of wavelength from peak location for wavelengths between 778.8 nm to 782.8 nm. Each discrete point is an average of 100
measurements of the spectral peak location determined from a Gaussian fit
to the raw spectrum. The solid line is a second-order polynomial fit, λ(nm)
= λ2 x2 + λ1 x + λ0 , where x is the pixel number and λ2 = −8.42237 × 10−8 ,
λ1 = 4.43609 × 10−3 , λ0 = 777.948.
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J. D. White and R. E. Scholten
Rev. Sci. Instrum. 83, 113104 (2012)
384.236
0.03
Known frequency (THz)
Wavelength deviation (nm)
113104-3
0.02
0.01
384.234
384.232
384.230
384.228
0
384.228
16
18
Temperature
20
22
°C
FIG. 4. Temperature dependence of the wavelength offset calibration. Temperature changes affect the grating pitch, producing a nearly linear offset over
the tested range.
structural stability of the camera mount in relation to the grating and fiber input. The most significant environmental factor
is temperature, which directly affects the grating line spacing
through thermal expansion of the substrate. The variation was
measured (Fig. 4) to be approximately −4.3 pm/K, which
corresponds to a grating spacing variation of 7.7 × 10−6 /K, in
good agreement with the thermal coefficient of expansion for
the BK-7 borosilicate glass of our grating (7.1 × 10−6 /K).
In addition, temperature, pressure, and humidity affect
the refractive index of the air and hence the effective wavelength. For typical laboratory conditions (20%–80% RH), the
effects of variations in humidity are below the precision of the
spectrometer. The refractive index ntp corrected for temperature and pressure is then sufficiently well approximated by18
ntp = 1 +
(1.04126 × 10−5 )p
(ns − 1),
1 + 0.003671T
384.230
384.232
384.234
384.236
Measured frequency (THz)
(3)
where T is temperature in ◦ C, p is pressure in Pa, and ns is
the refractive index at 15 ◦ C and 1 atm (1.01325 × 105 Pa);
ns = 1.000275163 at λ = 780 nm. Under these conditions,
the wavelength variations with temperature and pressure are
approximately 1 pm/◦ C and 1 pm/500 Pa. We used a consumer
“weather station” to measure temperature and pressure with
0.1 ◦ C and 100 Pa resolution to determine the corrected in
vacuo wavelength via Eq. (3).
FIG. 5. Known and measured frequencies for the rubidium D2 hyperfine
transitions compared to a measured saturated absorption spectrum. The
horizontal error bars indicate the spectrometer wavelength uncertainty of
±0.7 pm.
ple wavelengths simultaneously. ECDLs will often simultaneously support two or more closely-spaced longitudinal cavity
modes with the total output power split between modes such
that the effective power is substantially reduced, yet without the multimode operation being readily apparent. Figure 6
shows an example with two modes separated by 40 GHz,
which corresponds to the free spectral range of the bare diode;
that is, the cavity formed by the front and rear facets of the
laser diode semiconductor.
The spectrometer can also be effective for undergraduate teaching laboratories, where the high resolution and sensitivity allow measurements of atomic structure such as the
sodium doublet spacing, again using the bare single mode
fiber without collection lens, in this case simply placed near
a sodium discharge lamp. Other appropriate experiments
might include measurement of the hydrogen/deuterium isotope shift19 or measurement of the vibrational constant of the
cesium dimer ground state.20 Note that calibration of the separation between lines depends on the focal length of the lens
and the grating spacing, which can be measured using a reference at a very different wavelength.
The wavelength range of the device as configured in
Fig. 1 has been sacrificed to achieve high resolution, but by
rotation of the 1800 /mm grating alone the device can access any wavelength between the 370 nm wavelength used
1
A spectrometer of this precision is particularly useful
when tuning an extended-cavity-diode laser system to atomic
transitions. At a wavelength of 780 nm, an uncertainty of
0.7 pm corresponds to 350 MHz, well below the Doppler
width of absorption lines in rubidium vapor. The spectrometer can then be used to tune the laser unambiguously to
the different hyperfine transitions in the rubidium D1 and
D2 manifolds. Fig. 5 shows wavelength measurements using a laser1 frequency-locked to four 85 Rb and 87 Rb hyperfine
transitions around 780 nm with locking stability better than
±1 fm(0.5 MHz).
A particular advantage of a spectrometer in comparison to interferometric wavemeters is the ability to see multi-
Relative intensity
IV. APPLICATIONS
780
0
776
780.1
777
780.2
778
780.3
780.4
779
780
Wavelength
λ (nm)
781
782
FIG. 6. Sample of spectrum for ECDL operating in multiple longitudinal
modes of the semiconductor diode cavity (1 mm length, 40 GHz mode spacing). Inset detail shows clear separation of the two modes.
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113104-4
J. D. White and R. E. Scholten
in Yb+ ion trapping21 (θ 1 = 2.9◦ ) and the 960 nm which is
used via second harmonic generation to access Rydberg states
in rubidium22 (θ 1 = 47.4◦ ). We have also successfully used a
wireless internet camera to create a network-connected device
and a digital single lens reflex camera with 24 mm wide sensor which provided 28 nm range, sufficient to acquire the full
spectrum of a femtosecond laser.
V. CONCLUSION
The spectrometer is compact, readily constructed from
commonly available components without requiring special
machining, and yet sufficient to resolve the hyperfine spectrum of the rubidium absorption spectrum with only 1 pW
of optical power. In a research environment, these features
would allow incorporation of a separate spectrometer to monitor each laser in a complex laser atom cooling experiment. In
the undergraduate teaching context, construction and calibration of the spectrometer can provide a useful learning experience in itself and also a precision apparatus for probing the
quantum nature of atomic structure.
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