Detector Properties To Instrument Science Objectives

By analyzing the science tradeoffs that will occur when detector performance is less than (or better than) the instrument specification, a figure of merit can be established for each tested detector. This will allow an unambiguous comparison of different detectors and detector technologies to be made and will reflect the degree of suitability of any particular detector to the instrument science objectives. To derive the figure of merit for each detector, metrics are obtained from direct measurements of a detectors' performance, which are then normalized to a typical operational model of an instrument observational unit. In this paper, five metrics are considered in the figure of merit for a detector. These are cadence (i.e. Observed sky / time), observed optical quality, observational depth, photometric accuracy, and observatory efficiency. The metrics for each tested detector are then presented as a three-axis histogram to aid in the visual identification of areas of merit or deficiency for a particular detector. The X axis of the histogram represents the five different metrics, the Y axis is the calculated metric score and the Z axis is the wavelength dependence of each metric. A figure of merit value is then derived from the five metrics according to a weighted product that reflects the priorities of each one towards the science objectives of the instrument. In this way detector type suitability to a particular objective is presented by using either measured, published, or projected performance values. When delivery of the chosen detectors begins, each detector is tested and the individual suitability is determined using the same criteria. In this way, the suitability of different detector technologies, individual detector test results, and detector testing results from different laboratories can be directly compared.

2.1 Normalization of Metrics

To provide fair weighting of each metric to the overall figure of merit value obtained for a detector, the conditions for calculating them are normalized to a 'standard' observation on a 'standard' sky using a 'standard' telescope. Nominal values for these standards are derived from expected performance figures of the instrument and telescope in the wavelength regions of interest. For the purpose of this paper, the standards are derived with respect to the LSST mission and the nominal values for these taken from the LSST Exposure Time Calculator. Detector performance parameters that are measured but not included within the calculation of metrics must be proven to be at a value that does not interfere with the figure of merit i.e. they must be 'in the noise' or not limit the measurements used to derive the metric.

2.1.1 Standards

Standard Observation

Five 10 second integrations, one each using the UBVRI band pass filters, on a standard sky through a standard telescope. Seeing for the standard observation is set to 0.8 arcsec rms. Table I defines these properties.

Table I - Standard Observation

Defined quantities

Symbol

Units

Integration time

T

seconds

Seeing

S

arc sec rms

Required SNR for observation

Snr

A standard sky is described as a plane peppered with 10th and 24th mag stars at all wavelengths and with representative sky brightness in bands. Table II define these properties.

Table II - Standard Sky

Defined quantities

Symbol

Units

Bloom star

Bm

Vmag

Object star

Om

Vmag

Sky brightness

Sm

Vmag

Bloomstars in each arcminute2

Bn

stars

Standard Telescope

A standard telescope is established as a 7 meter diameter effective aperture telescope with a nominal throughput of 85% at all wavelengths. The plate scale is set to 20 arcsec / mm and a three degree2 field of view is available. Table III defines these properties.

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Peter Moore and Gustavo Rahmer

Table III - Standard Telescope

Defined quantities

Symbol

Units

Free aperture

A

meters

Plate scale

Pm

arcs / mm

Throughput

E

%

Field of view

Fov

arc degrees2

2.1.2 Metrics

2.1.2 Metrics

Due to space limitations of this paper, only two metrics, Cadence and Optical depth, of the five total will be described here. The missing metric calculations are performed in a similar manner to those described here.

Cadence is the ratio of time between that required for a standard observation using the instrument detector specifications and the time calculated to achieve the same observation in detector testing. The cadence metric is shown in Table V and is derived using the parameters defined in Table IV.

Table IV - Cadence Metric Parameters

Measured quantities

Symbol

Units

Pixel size

Ps

microns

Bright pixels

Pb

% of pixel count

Dark pixels

Pd

% of pixel count

Traps

Pt

rows and columns

Readout noise

Nrd

e- rms.

Quantum efficiency

QX

% efficient at X

Readout time

Tr

seconds

Fill factor

F

% of detector area active

Dark current generation

Di

e- / pixel / sec

Full well

Fw

e-

Blooming control

Bc

% Fw before bloom occurs

Seeing correction

Sc

% reduction of seeing disk

Observation depth (MUd, MBd, MVd, MRd, MId) The difference in observed magnitude between the calculated magnitude achieved in a standard observation using the instrument detector specifications and that calculated using measured detector parameters. This metric does not consider field coverage. The observational depth metric is shown in Table VII and is derived using the parameters defined in Table VI.

Table V - Cadence Performance Metric (Mc) Development Using the quadratic of form: Results in:

a = QX'Of J b=-Snr3QX(OfSf ) c = -Sur 3 + PnNt 1 x = T

Table VI - Observational Depth Metric Parameters

Measured quantities

Symbol

Units

Pixel size

Ps

microns

Quantum efficiency

QX

% efficient @ X

Readout noise

Nrd

e- rms

Fringing

FrX

% rms mean signal @ X

Image latency

Li

e-

Dark current generation

Di

e- / sec / pixel

Seeing correction

Sc

% reduction of seeing disk

Table VII - Observational Depth Metric (Md) Development Using the quadratic of form: Results in:

_ - b ± y/b1 - 4ac * 2a where : a = QX1 b = -Snr 2QX

2.1.3 Derived Values

These values are derived from the predicted first order performance metrics of the instrument plus telescope and used to define the operational conditions of the detectors under review.

Table VIII. Derived Performance Parameters

Table VIII. Derived Performance Parameters

2.1.4 Metric Calculation Methods

The calculations for deriving the various metrics are performed with an Excel spreadsheet. Graphics are used to display the results and enable a rapid and decisive estimation of science performance based on detector performance.

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