**5. Acknowledgment**

154 Advanced Holography – Metrology and Imaging

transmittance object, illuminated by a plane wave E�, then the output field after diffraction

E(x) = E� � T(x�)H(x, x�; n�l� + n�l�, l�/n� + l�/n�)dx�. (33) When the net diffraction length in the successive propagation is null, i.e. l�/n� + l�/n� = 0,

E(x) = E� exp[ik�(n�l� + n�l�)] T(x). (34)

To better compare the two schemes, in Fig. 13(b), the interferometer is opened out and the two arms are set along a line. We can see that the joint diffraction through the two arms is

Recently, various approaches for invisibility cloaking and transformation optics in complementary media with positive and negative refraction materials have been proposed, which can in theory accomplish exact optical cancellation between the object and its counterpart (Lai et al., 2009a, 2009b). In light of the similarity of time-reversal diffraction between incoherent interferometry and negatively refracting media, using the present scheme, we have conducted proof-of-principle experimental demonstrations of the theoretical proposals (Zhang et. al., 2010; Gan et al., 2011). The physical analogue between the two different systems may provide a convenient research platform. Moreover, a form of nonlocal imaging as well as interference effects that were previously regarded as the signature of two-photon entanglement or intensity correlation of thermal light can now be realized in incoherent interferometry, which is associated with the first-order field

Interference effects in incoherent interferometry show different physics from that in coherent interferometry. In the latter case, two interfering fields have well-defined spatial distributions, whereas in the former case, these fields fluctuate randomly in space and the interference pattern appears only in the statistical average. Furthermore, incoherent interference relies entirely on the first-order spatial correlation of the two fields, so the object information is contained in the joint diffraction of the two fields. For certain optical geometries, phase reversal diffraction can occur through the first-order spatial correlation of incoherent light, thus providing a method of wave-front recovery without using a lens, and

Incoherent interferometry as a novel interference mechanism exhibits richer phenomena than the coherent type. Since it is not dependent on spatial coherence, the present method may find potential application in holography and other interference technologies, especially in those areas where a coherent source is unavailable. Incoherent holographic interferometry is fundamentally different from the previously known incoherent holography, while it can

E(x) ∝ E�exp [ik�(n�l� + n�l�)] � T(x�)G(x − x�, l�/n� + l�/n�)dx�, (35)

Otherwise, Eq. (33) represents Fresnel diffraction with a diffraction length of l�/n� + l�/n�

then H(x, x�; n�l� + n�l�, 0) = exp[ik�(n�l� + n�l�)] δ(x − x�) and we have

is written as

which has the same form as Eq. (27)

comparable with the geometry in Fig. 13(a).

correlation (Gao et al., 2009; Gan et al. 2009).

also a means for optical transformation.

play the same role as coherent holography.

**4. Conclusion** 

The authors thank L. A. Wu for helpful discussions. This work was supported by the National High Technology Research and Development Program of China, Project No. 2011AA120102 and the National Natural Science Foundation of China, Project No. 10874019.
