Direct-to-digital holography reduction of reference hologram noise and fourier space smearing

A method, comprising reducing smearing in Fourier space including:

• recording a plurality of reference holograms;
• processing the plurality of reference holograms into a corresponding plurality of reference complex image waves including Fourier analyzing the plurality of reference holograms by transforming axes of the plurality of reference holograms in Fourier space to sit on top of a heterodyne carrier frequency defined as an angle between a reference beam and an object beam and applying a digital filter to cut off signals around an original origin and then performing an inverse Fourier transform;
• transforming the corresponding plurality of reference image waves into a reduced noise reference complex image wave by calculating an average of the plurality of reference complex images;
• recording a hologram of an object;
• processing the hologram of the object into an object complex image wave;
• and
• dividing the complex image wave of the object by the reduced noise reference complex image wave to obtain a reduced smearing object complex image wave.

A method, comprising reducing smearing in Fourier space including:

• recording a plurality of reference holograms;
• processing the plurality of reference holograms into a corresponding plurality of reference complex image waves;
• transforming the corresponding plurality of reference image waves into a reduced noise reference complex image wave;
• recording a hologram of an object;
• processing the hologram of the object into an object complex image wave;
• dividing the complex image wave of the object by the reduced noise reference complex image wave to obtain a reduced smearing object complex image wave;
• performing a Fourier transform on the reduced smearing object complex image wave;
• correcting aberration with a corresponding phase plate;
• and
• performing a consecutive inverse Fourier transform to yield an optimized αφ(x,y) that is substantially equal to φobj(x,y).

A method, comprising reducing smearing in Fourier space including:

• recording a plurality of reference holograms;
• processing the plurality of reference holograms into a corresponding plurality of reference complex image waves;
• transforming the corresponding plurality of reference image waves into a reduced noise reference complex image wave;
• recording a hologram of an object;
• processing the hologram of the object into an object complex image wave;
• dividing the complex image wave of the object by the reduced noise reference complex image wave to obtain a reduced smearing object complex image wave;
• performing a Fourier transform on the reduced smearing object complex image wave;
• processing the Fourier transformed reduced smearing object complex image wave with a synthetic aperture in Fourier space that does not accommodate smearing in Fourier space due to non-planar illumination;
• and
• performing a consecutive inverse Fourier transform to yield an optimized Δφ(x,y) that is substantially equal to φobj(x,y).