ZEISS
Hardware Aspects
ELYRA 7
10
000000-2262-999
03/2019 V_02
The interference of the structured light with object
structures requires that at least part of the light is
coherent and leads to so called Moirè fringes
whose pattern has a longer periodicity and hence a
lower space frequency compared to the object
(Fig. 3).
Each sample or object structure can be regarded as
a superimposition of many grids. Due to the
structured illumination the object frequencies will
be shifted to lower frequencies due to the Moiré
effect. Therefore high frequencies that normally
cannot be collected by the system can be
transmitted due to their shift into lower
frequencies.
Due to the diffraction nature of light the
modulation grid frequency cannot have a
periodicity that is smaller than half the wavelength,
so resolution enhancement can be a maximum of
two fold in each lateral and axial direction.
Due to the frequency shift the image frequencies
are composed of non-shifted and shifted object
frequencies and hence their contribution has to be
determined.
A coherent image generated with a sinusoidal line grid pattern has generally 3 different orders created by
interference: the 0
th
order from the 0
th
order non-diffracted beam, the 1
st
order created by interferenes of
the
±
1
st
order diffraction beams with the 0
th
order non diffracted beam (frequencies shifted by half the
modulation frequency) and the 2
nd
order created by the interference between the +1
st
order with the
– 1
st
order diffracted beam (frequencies shifted by the modulation frequency). (Fig. 2).
It is the 2
nd
order that contains the high frequency information for resolution enhancement in X,Y (Fig. 4).
The 1
st
order contains information for sectioning and better z-resolution.
To shift the frequencies to their correct location, a linear equation with 5 unknowns (2 x n-1, n=number
of different orders, which is 3 in the case of a line grid) has to be solved. This can be pixel wise
accomplished by recording 5 images with a phase shifted modulation pattern. Since resolution is
obtained only in the orientation of the grid pattern, the grid has to be rotated to obtain a nearly uniform
resolution in all directions. In generally one uses 3 rotations are sufficient. Hence, the reconstruction of a
Fig. 3
Moiré pattern generated by overlaying
two line grids – the lower periodicity of
the generated pattern is visible as
thicker lines
Fig. 4
Expansion of the transmitted frequencies – the cut-off frequency is
indicated by k
0
, phase shifts by
Φ
and rotations by
ρ
; only the shift by
the modulation frequency is shown as this contains the high
resolution information