Astronomy - USA (2020-06)

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Signal Point-spread^ function

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56 ASTRONOMY • JUNE 2020

technique that eliminates any
noise when making the mea-
surement. After that, I need
to minimize other sources of
error. This is done using tech-
niques that any amateur can
learn; you may already be
using some if you image.
The first technique, called
aperture photometry, involves
performing a differential pho-
tometric measurement using
an aperture to restrict the light
to a given area of the detector
(a CCD or CMOS chip) cen-
tered on the star. Another

area, called the annulus, which
surrounds the aperture, allows
you to measure the sky bright-
ness. The individual bright-
ness of a star is measured by
subtracting the sky measure-
ment from that of the star (see
“Starlight minus sky” on
page 54). After these values are
obtained for the target and
comparison stars, the differ-
ence between them results in a
series of differential photomet-
ric measurements that are
used to create the light curve.
This effectively cancels out
any brightness changes, such
as dimming by a passing thin

cloud, that affect all the stars

in an individual image.

Additionally, there are

three types of error you must

correct or minimize. One is

systematic error (image defects

and errors). The other two are

random errors (shot noise

error and scintillation error).

For the systematic error, I use

the standard method of cali-

bration used by most astro-

photographers when they

image deep-sky objects. The

RAW images are calibrated

prior to doing any measure-

ments using aperture photom-

etry. This corrects them for

bias (readout) noise, dark

(thermal) noise, and differ-

ences in the detector’s pixel

response. Applying these cor-

rections takes care of most of

the noise as well as image

defects, such as vignetting and

dust, within the camera and

optical train.

Nevertheless, even after

calibration, a small source of

systematic error remains. This

is called residual calibration

error (RCE), which involves

small variations from pixel to

pixel. You can eliminate RCE

by keeping the star on the

same pixels over several hours.

Although it typically totals

less than a half percent, it is

a significant portion of the

error when you want to reveal

exoplanets. RCE can be

reduced through a high level

of control when tracking a

target accurately for long

periods. Unfortunately, this

can be expensive and time-

consuming for most amateurs.

There are also several ran-

dom errors. When sampling

light, the photons arrive at

random intervals, causing

an error in the signal called

Poisson (shot) noise. Shot

noise is related to the particle

nature of light. When doing

photometry, we are counting

the number of photons that hit

each pixel. The detector con-

verts the photons to a numeric

value. Quantum efficiency of

cameras vary, but it can

exceed 75 percent of all the

photons hitting the chip. The

shot noise error value is pro-

portional to the square root of

the total count recorded. As

the number of photons col-

lected increases, so does the

signal-to-noise ratio, which

increases the shot noise accu-

racy (see “Signal beats noise”

at upper left). The overall mea-

surement, then, is limited only

by the scintillation error.

Scintillation is an error

that divides into short-term or

long-term. Short-term scintil-

lation noise is caused by

atmospheric conditions that

make stars appear to twinkle,

and is an indication of the

seeing (atmospheric steadi-

ness). Until recently, the only

way to significantly reduce

short-term scintillation error

was to avoid times and/or

locations where it was high.

Long-term scintillation noise

is a slow change in the star’s

brightness caused by the slow

movement of high clouds and

variations over time in the

sky’s brightness and haze

(transparency). It can be

largely avoided by taking

observations on clear nights.

A new method for

high-precision

photometry

A long-used technique for

doing high-precision pho-

tometry is called the defocus

method. Defocusing the tele-

scope increases the shot noise

precision of the measurement

by spreading the light out

The more photons a detector collects, the better the signal-to-noise

ratio will be. ASTRONOMY: ROEN KELLY AFTER JERRY HUBBELL

Collecting data through a defocused telescope produces a bell-

shaped point-spread function. RACHEL KENOPA GOOD

Today, just about anyone can make precise

measurements of stars from their backyard.

SIGNAL BEATS NOISE OUT OF FOCUS