Phase Unwrapping Problems in Digital Holographic Microscopy of Biological Cells - Biomedical Optical Phase Microscopy and Nanoscopy - page 138

0 or 1 depending on whether 2 ( x , y ) is positive or negative. Therefore,

subtracting the two phase maps and adding 2

ϕ 1 ( x , y ) 2 ϕ

whenever the difference is negative
effectively yields a new phase map, which corresponds to the beat wavelength

π

Λ 12 .

Figure 7.11 shows the phase images of the USAF resolution target imaged at a slight angle.
The images produced with a single wavelength exhibit multiple phase steps (see
Figure 7.11A and B ). By comparing the phase images from each wavelength, the 2 π phase

ambiguities can be resolved. For λ 5 633 and λ 5 532 nm, Λ 5 3334 nm, which is high 1 2 12

enough to remove the discontinuities (see Figure 7.11C) .

The negative aspect of this method is that the phase noise is also amplified by the same
factor as the range. However, one can then use this dual-wavelength “coarse” map as a
guide, together with one of the original phase maps ( 2 ), to produce the low noise

“fine” phase map [10] . If the noise in the coarse phase map is too excessive, some of the
single wavelength segments might still end up being vertically shifted from its correct
position by a single wavelength, creating phase image artifacts. These errors can then be
corrected in software by simply looking for such jumps and shifting them up or down [3] .
In comparison to the coarse map, the noise in the resulting fine map (see Figure 7.11D) is
much lower, while the axial range is still the same.

ϕ 1 or ϕ

3.142

− 3.142

(A) (B)

nm nm

800

600

600
400

400

200

200

0

000

− 200
− 400
− 600
− 800

− 200

(D)

(C)

− 400

Figure 7.11

Phase maps for (A) λ 1 5 532 nm and (B) λ 2 5 633 nm; (C) 3D rendering of synthetic dual-phase

map with beat wavelength Λ 12 5 3334 nm and (D) reduced noise fine map (the images are

174 μ m 174 μ m, 450 450 pixels).

3 3