  It is commonly accepted that optical sub-Rayleigh imaging has potential
application in many fields. In this Letter, by confining the divergence of the
optical field, as well as the size of the illumination source, we show that the
first-order averaged intensity measurement via speckle laser illumina- tion can
make an actual breakthrough on the Rayleigh limit. For a high-order algorithm,
it has been reported that the autocorrelation function can be utilized to
achieve the sub-Rayleigh feature. However, we find that this sub- Rayleigh
feature for the high-order algorithm is limited only to binary objects, and the
image will be distorted when a gray object is placed. This property encourages
us to find the physics behind the high-order correlation imaging algo- rithm.
We address these explanations in this Letter and find that for different types
of high-order algorithm, there is always a seat in the right place from the
cross-correlation function.
