Extended depth of field optical systems

An imaging system having insensitivity to misfocus, the imaging system being characterized at least by an ambiguity function and a point spread function (PSF), which ambiguity function is a function of a normalized spatial frequency parameter u and a misfocus parameter ψ, and which PSF is also a function of at least the misfocus parameter ψ, the imaging system comprising:

• at least one lens, an optical mask and a detector that cooperate to image light from an object to form a stored image, which lens is characterized by at least a length L, a focal length f, a front principal plane and a rear principal plane, and which light is characterized by at least phase and a wavelength λ the optical mask modifying the phase such that a main lobe of the ambiguity function is broader for a given range of ψ at a given value of u, and the PSF has a functionally different form, in comparison to a main lobe of an ambiguity function and a PSF, respectively, characterizing the imaging system without the optical mask for that given range of the misfocus parameter ψ,defined by the equation:
• ⁢
• ψ
• =
• L
• 2
• 4
• ⁢
• π
• ⁢
• ⁢
• λ
• ⁢
• (
• 1
• f
• -
• 1
• d
• o
• -
• 1
• d
• i
• )
• ,
• where dois a distance from the object to the front principal plane and diis a distance from the rear principal plane to the detector.

A method for imaging, in an optical system characterized by at least an ambiguity function and a point spread function (PSF), which ambiguity function is a function of a normalized spatial frequency parameter u and a vertical variable v related to a misfocus parameter ψ, and which PSF is at least a function of the misfocus parameter ψ, the method comprising:

• imaging light from an object to form an optical image, which light is characterized by at least phase;
• and
• detecting the optical image to generate a stored image,
• wherein imaging includes modifying the phase, such that a main lobe of the ambiguity function is broader in v for a given value of u, and the PSF has a functionally different form for a given value of ψ over an extended depth of focus that is larger than a depth of focus formed without modifying the phase, in comparison to a main lobe of an ambiguity function and a PSF, respectively, characterizing the optical system without modifying the phase for those given values of u and ψ.

An imaging system, comprising:

• a lens and an optical mask that cooperate to image light from an object to form an optical image having a range of spatial frequencies that is limited by an aperture of at least one of the lens and the optical mask, which light includes at least phase;
• and
• a detector for detecting the optical image over the range of spatial frequencies to generate a stored image,
• wherein the imaging system is characterized at least by an ambiguity function and a point spread function (PSF), which ambiguity function is a function of a normalized spatial frequency parameter u and a vertical variable v related to a misfocus parameter ψ, and which PSF is at least a function the misfocus parameter ψ, and
• wherein the optical mask is configured for modifying the phase without reducing the range of spatial frequencies, such that a main lobe of the ambiguity function is broader in v for a given value of u and the PSF has a functionally different form for a given value of ψ, in comparison to a main lobe of an ambiguity function and a PSF, respectively, characterizing the imaging system without the optical mask for those given values u and ψ, over an extended depth of focus larger than a depth of focus without the optical mask.

A method for imaging light from an object to form an image in an optical system, which light includes phase and which imaging system is characterized at least by an ambiguity function and a point spread function (PSF), which ambiguity function is a function of a normalized spatial frequency parameter u and a vertical variable v related to a misfocus parameter ψ, and which PSF is at least a function of the misfocus parameter ψ, the method comprising:

• forming the image;
• and
• detecting the image over a range of spatial frequencies,
• wherein forming the image includes modifying the phase without reducing the range of spatial frequencies, such that a main lobe of the ambiguity function is broader in v for a given value of u and the PSF has a functionally different form for a given value of ψ, in comparison to a main lobe of an ambiguity function and a PSF, respectively, characterizing the imaging system without modifying the phase for those given values u and ψ, over a range of object distances between the object and the imaging system.

An imaging system characterized at least by an ambiguity function and a point spread function (PSF), which ambiguity function is a function of a normalized spatial frequency parameter u and a misfocus parameter ψ, and which PSF is also a function of at least the misfocus parameter ψ, the imaging system comprising:

• a lens and an optical mask that cooperate to image light from an object to form an optical image, which light is characterized by at least phase;
• and
• a detector for detecting the optical image over a range of spatial frequencies to form a detected image,
• wherein the optical mask is configured for modifying the phase such that a main lobe of the ambiguity function is broader for a given range of ψ at a given value of u and the PSF of the system has a functionally different form, in comparison to a main lobe of an ambiguity function and a PSF, respectively, characterizing the imaging system without the optical mask for that given range of the misfocus parameter ψ and over a range of object distances from the object to the system.