The images above illustrate the effect of lensing of relatively low spatial frequency MBR fluctuations by higher frequency projected density fluctuations.

The upper left image shows a gaussian filtered gaussian random field which represents the surface potential of the lensing field.

The upper right panel is a gaussian filtered gaussian random field with a larger coherence scale which represents the unlensed MBR fluctuations.

The lower left panel shows how the MBR fluctuations would actually appear after lensing (with a somewhat unrealistically large amplitude for the lensing deflection it should be admitted....)

The lower right panel shows a hig-pass filtered version of the lensed MBR fluctuations, which emphasises the non-gausssian nature of the lensing induced fluctuations.

What we are seeing here is a coupling between the gradient of the unlensed MBR and the projected density fluctuations; the lens induced fluctuations take the form of a gaussian random field modulated by the amplitude of the angular derivative of the low-frequency MBR fluctuations.

This characteristic non-gaussianity may be useful for discriminating between lening induced and intrisic MBR fluctuations at high frequency.

Grey-scale version:

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e-mail: kaiser@ifa.hawaii.edu