ANITA Note #101
Observation of Light Transmission Through Randomly Rough Glass
Surfaces Up to and Beyond the Critical Angle of the Glass-Air Interface
Mark Harrison, Martin Griswold, David Saltzberg (UCLA)
February 17, 2016
Abstract
When light propagates through a medium and encounters a boundary to a medium with a
lower index of refraction, it will totally internally reflect if the angle of incidence is larger
than the critical angle as defined by Snell’s Law. We have added to our roughness
teststand the ability to probe incident angles up to and beyond the critical angle. In this
series of experiments, we show that if the interface between the two media is a random
rough surface with surface features on the order of the wavelength of the incident light,
transmission of light will be observed at angles of incidence well beyond the critical
angle. For light not beyond the critical angle, the peak does not obey Snell’s law and
is not bent as far away from the normal. Light that would have passed through
specularly is spread into a larger solid angle, with less intensity at any given angle. These
two properties are relevant to the ANITA experiment because we measure the
transmission of radiation through a rough surface.
Setup
This experiment was largely identical with the one described in a previous note1 with one
major difference. In order to have light incident upon the interior surface of the glass at
angles larger than the critical angle, we affixed a half-cylinder lens so that incident laser
light would not refract when entering the glass (Fig. 1).
Angle of
photometer, θp
Glass Plate or Diffuser
Polarizer
Laser
Photometer
Half-cylinder lens
Angle of
incidence, θi
Figure 1: Experimental Setup
Daub, Everson, et al., “Optical Modeling of the Effect of Surface Roughness on Detection of Signals from
Within the Ice with ANITA.” March 10, 2006. http://charm.phys.hawaii.edu:8080/anita_notes/77
1
In this setup, the laser was a He-Ne type with a wavelength of 633 nm and 580 uW power
output. The polarizer was oriented so that the laser light is incident upon the glass
surface with s-polarization (out of the page in the above diagram). We rotated the lensglass element about the center of curvature of the half-cylinder lens to that the laser beam
was always normal to the surface of the lens. The photometer was moved along a line
perpendicular to the incident laser in order to measure the scattering of light after passing
through the optical elements. Not shown are extra masks and apertures used to block
extraneous reflections from the various elements.
Glass has an index of refraction of 1.5. Accordingly, the critical angle is 41.8º.
Diffuser Surface Features
Using a VEECO Dimension 3100 Atomic Force Microscope, we characterized the
surface features of the diffusers. An explanation of the meaning of the grit numbers
appears in the previous note1. Briefly, the inverse of the grit number is the diameter in
inches of the largest particle of grit used to grind the diffuser.
Each scan produced a 256 × 256 array of heights. Table 1 below gives the RMS heights
and correlation lengths of the two diffusers over various scan areas. The RMS height is
simply the RMS of the distribution of every height in the scan. The RMS correlation
length was found by calculating the two-dimensional autocorrelation function of the
height data and finding the average half-width at half-maximum (HWHM). Assuming a
roughly Gaussian shape for the curve, we divided the HWHM by 2 ln 2  2 to get what
we call the RMS Transverse Correlation Length. Images of the diffuser surfaces appear
in figures 2-4.
Grit
Scan size (μm)
RMS Height (μm)
400
50 × 50
75 × 75
100 × 100
1.0
1.2
1.4
RMS Transverse
Correlation Length (μm)
2.5
3.1
5.1
10 × 10
20 × 20
30 × 30
50 × 50
0.32 – 0.34
0.41 – 0.57
0.50 – 0.54
0.50 – 0.60
0.9 – 1.3
1.2 – 4.3
1.3 – 3.1
4.1 – 7.7
10 × 10
20 × 20
30 × 30
50 × 50
0.23 – 0.26
0.28 – 0.42
0.36 – 0.45
0.42 – 0.47
0.4 – 0.5
0.7 – 1.1
0.9 – 1.2
3.8 – 4.1
1000
1500
Table 1: Feature sizes of ground glass diffusers
We performed scans at two different locations for the 1000- and 1500-grit diffusers to get
an idea of the homogeneity of the surface roughness. Only one set of scans was
performed on the 400-grit diffuser because of time constraints. Within a factor of 2, the
feature sizes are relatively homogenous across the surface of the diffuser.
Since the ratio of the Cherenkov radiation wavelength to the laser’s wavelength is about
106 (~0.5 m to ~0.6 μm), these diffusers can be said to model Antarctic features with
sizes given by Table 1 in meters. For example, the 1500-grit diffuser models an
Antarctic terrain with an RMS height of 0.23 – 0.47 m and RMS transverse correlation
length of 0.4 – 4.1 m. 2
Results
Figures 5-7 show comparative charts of the light transmissions at 0º, 40º, and 70º angle of
incidence (finer data could be taken in the future if deemed helpful). The flat glass
refracted light according to Snell’s Law at angles of incidence smaller than the critical
angle and showed no transmission of light at angles larger than the critical angle. The
diffusers, however, skewed the distribution of light towards the normal of the diffuser
surface and continued to transmit light even when the laser light was incident at angles
much larger than the critical angle.
At angles of incidence that are not totally internally reflected, the 1500-grit diffuser has
the highest peak transmission and the 400-grit diffuser lets through the lowest. At angles
that are totally internally reflected in flat glass, these observations are reversed.
Conclusion
Our experiments demonstrate that a rough interface will transmit light incident upon it at
angles of incidence normally totally internally reflected by a flat surface. Further studies
and other simulations incorporating this data are required to determine the significance of
these findings to the ANITA project. Although we did not observe any differences
between a coherent and incoherent light source, perhaps some difference could be
observed between this continuous wave source versus a pulsed source. For ANITA we
would like to quantify the compensating effects of larger aperture due to viewing beyond
TIR vs. the diffusion of the specular power, with loss of intensity, into a larger solid
angle. Figures 5-7 show that for our diffuser the latter effect is dramatic, but this
diffuser is also a significant overestimate of the expected roughness. The lower index of
refraction of snow (~1.3), where present, might also reduce these effects.
2
This can compared to continental data taken from a variety of traverses (mostly near the coasts) and
backscatter properties of radar altimetry (80% of the surface) from satellites. Near the coasts more
roughness is observed due to katabatic winds and snow accumulation. Large scale (>30cm) features occur
most often near the coasts but with smaller frequency than our diffuser. Smaller features (~3cm) appear
most everywhere but are smaller than the corresponding features even on the 1500 grit diffuser. So our
diffuser is about an order of magnitude rougher than much of the ice we will be viewing. We plan to post
a literature summary of traverse and radar-altimeter data in the elog soon.
Figure 2: Surface of a 400-grit diffuser
Figure 3: Surface of a 1000-grit diffuser
Figure 4: Surface of a 1500-grit diffuser
Figure 5: Comparison of scattering at 0º incidence
Figure 6: Comparison of scattering at 40º incidence
Figure 7: Comparison at 70º incidence (well beyond the critical angle where flat glass does not
transmit light)