2.1

Design

The test bench is designed to allow both measurements (staring & TDI modes) in the most similar configuration in order to avoid bias when comparing them.

To estimate the MTF, several methods exist. For this test, we do not search for an MTF evaluation at all spatial frequencies. The frequency of interest is the specific Nyquist frequency:

with a = pixel pitch

One easy method for the MTF measurement at a defined frequency is the evaluation of the contrast. Here, we use an object made of black & white fringes. At Nyquist frequency, the image of a fringe has the same width as a pixel. The spatial resolution is directly linked to the capacity to distinguish the black from the white.

The image of this object on a pixel as a function of its position is a sine wave :

From that result, the Contrast Transfer Function (CTF) is easily calculated :

with ϕ_dark : dark signal level

The set-up is the following [Fig.2]

Fig. 2.

contrast evaluation method

We use an integrating sphere as light source, the object is in the focal plane of the collimation lens. A mirror is mounted on a rotary stage that will simulate the Earth scrolling. A focalization lens allows the image to be formed on the detector. The object is mounted on a 3 axis motorized system.

For the static measurement, the object is moved step by step following the Y axis. For every step, the level on the chosen pixel is stored.

For the dynamic measurement, the rotary stage is turning at the defined speed (the one corresponding to the detector charge transfer). The acquisition is triggered by the rotary stage. The rotary stage being synchronized with the detector charge transfer speed, an acquisition is composed of a series of maxima & minima, the levels of these max & min depending on the phasing of the fringes vs. the detectors lines. The object is moved step by step following the Y axis to change the phasing. For each step, an acquisition is performed.

Note:

2.2

Dimensioning

The test bench dimensioning activity takes into account:

the 3D modelling has been used to help in establishing the configuration [Fig. 4].

Fig. 3.

Test bench schematic

Fig. 4.

Test Bench 3D modeling

This allows to define a coarse location for each element, avoiding the mechanical conflicts.

The bench MTF has an impact on the precision we will get. In fact, the measured MTF is the product of the bench MTF and the detector MTF. The better the bench MTF is, the better the precision will be. Optical simulation is used to select the configuration

An accuracy budget is made to evaluate the influence of each parameter and consequently to put the stress on the tightly points.

The most critical point is related to the speed stability. In fact, in the TDI mode, the MTF evaluation is impacted by the effect of the inaccuracy in the image and charge transfer speeds synchronization (desynchro MTF) and by the scrolling effect (smearing MTF):

With the following hypothesis:

we get the formulae:

and

We analyse the impact of the non perfect synchronisation of the image speed :

with

and we define m by

The conclusion of the calculation is:

This impact is greatly increased as we want to make an average on values get on n fringes to increase the signal to noise ratio (SNR). With m defined by (8), this factor is equal to :

Finally, in order to get a good precision and to allow a good SNR, we specified the need for a speed stability better than 0.1%.

The rotary stage is consequently the key element of the bench. It should allow:

The final choice has been made for a high precision air-bearing rotary stage with a fast control electronic (maximum resolution =1.25.10^-6 ° !!).

The accuracy budget give also the sensibility to the optical adjustments. The main points are the magnitude adjustment and the object tilt.

3.1

Alignments

The detector working in staring mode, the alignment is performed. The reference is the rotation axis of the mirror.

The fine positioning in tip/tilt has been performed by auto-collimation on the detector and on the successive optical & mechanical parts (mirror, detectors, lens holders and object).

For the magnitude very precise adjustment an innovative method has been used. This is based on CTF acquisition for different position of the object, looking on the de-phasing on the object position corresponding to the extrema.

Fig. 6 shows a zoom on the image of the fringes on the detector when the alignment, the magnitude, and the focus are adjusted :

Fig. 5.

Test Bench photograph

Fig. 6.

image of the fringes aligned with the detectors lines

Note about Fig.6:

This allows the MTF in the staring mode to be evaluated.

Once the static alignment is performed, the adjustments in the dynamic mode are made:

The measurements show a very sane behavior of the test bench. In fact [cf. Fig. 7] :

Fig. 7.

Test Bench sensitivity to the speed 23.4795 vs. 23.4800 °/s

A few explanation:

Fig.7. represents, for 2 different speed of the rotary stage, the contrast observed as a function of the run:

The contrast is changing from one run to the consecutive one due to a constant phase shift between the trig clock of the rotary stage & the main clock of the detector (the evolution of the contrast is not linked to a difference in speed between these two clocks).

The stability of this difference in time, and the reproducibility of the behaviour is representative of the test bench stability.

3.2

Results

a) capacity in doing MTF measurements in TDI mode The test bench has got a sane behavior and allows a great accuracy in the rotary stage speed setting. The main success criteria is nevertheless the capacity to make measurements in TDI mode. On Fig.8, we see one of the measurement, at the maximum contrast, for one specific column.

Fig. 8.

MTF in TDI mode – visualisation of object (400 fringes) + zoom in

When the sampling card receives the trigger from the rotary stage, 1000 acquisitions are launched, each 100µs. Each point on the graph results from the integration of the signal on 20 lines.

The stability of the maxima & minima between the first and the last fringes: demonstrate that:

b) reproducibility

One of the other very impressive result is the stability of the test bench in time and the reproducibility of the measurements.

On Fig.9, are shown 2 measurements made with a 15 days time interval. It deals with CTF values (Y-axis) as a function of the column number(X-axis).

Fig. 9.

reproducibility over 15 days of the CTF evaluation in the TDI mode

We can observe a extremely good over-positioning of the measurements points : maximum of difference in this case <0.6% !!

c) relative measurements: staring mode vs. TDI mode Measurements in TDI mode stand as a critical point as well for the accuracy of measurements and for the repeatability.

But the real success criteria is the ability to compare the measurement in staring mode versus the TDI mode. We reach a repeatability in the difference evaluation better than 1%.

From this point of view, the tests are successful too ! (values are not significant as they are really linked to the detector)

d) new perspectives

the test bench allowed also the characterization of the detectors TDI mode sensitivity to other parameters like wavelength, aperture, number of TDI lines, input light power, …

This drives to a global review of the tests during the integration & characterization of the instrument. The results allow in fact to define more precisely the tests configuration and to refine the success criteria.

Such tests could be generalized for the future generation of High Resolution detectors and extended to instruments.