Lens aberration correction in a doubly telecentric displacement sensor

A doubly telecentric imaging configuration for use in an optical encoder that senses displacements, the doubly telecentric imaging configuration including:

• a first portion comprising a first lens located at a first lens plane along an optical axis, a limiting aperture located at an aperture plane along the optical axis, a second lens located at a second lens plane along the optical axis, and a photodetector configuration located at a detector plane along the optical axis;
• a scale grating pattern located at a grating plane along the optical axis, the scale grating pattern extending along a measuring axis direction and having a grating pitch P;
• and
• an illumination source configured to illuminate the scale grating pattern with a first source light comprising light that is directed parallel to a first plane having a first nominal illumination angle θ relative to a plane that is normal to the measuring axis direction and parallel to the optical axis, the first source light having a wavelength L,
• wherein,
• the doubly telecentric imaging configuration is configured such that:
• an object point on the scale grating is imaged to a corresponding image point in the image on the photodetector configuration by light included in a first diffracted scale light arising at that object point, the first diffracted scale light arising at that object point comprising a +1st order light ray bundle, a −1st order light ray bundle, and a zero order light ray bundle arising from the first source light;
• the first diffracted scale light is transmitted through the first lens and toward the aperture plane;
• the limiting aperture spatially filters the transmitted first diffracted scale light and transmits that spatially filtered light to be included in a first image light, wherein the limiting aperture is configured to:
• block at least a majority of one of the +1st order light ray bundle, the −1st order light ray bundle, and the zero order light ray bundle at the aperture plane, and
• transmit at least a majority of the other two of the +1st order light ray bundle, the −1st order light ray bundle, and the zero order light ray bundle through the limiting aperture to define a pair of imaging ray bundles that to contribute to the first image light that reaches the corresponding image point;
• the first image light is transmitted through the second lens to form an image of the scale grating pattern on the photodetector configuration;
• the photodetector configuration provides a displacement signal that is responsive to the position of the image of the scale grating pattern relative to the photodetector configuration along the measuring axis direction;
• and
• a first member of the pair of imaging ray bundles passes through a first portion of the first lens and a second portion of the second lens, a second member of the pair of imaging ray bundles passes through a second portion of the first lens and a first portion of the of the second lens, and the first portions of the first and second lenses have nominally the same first optical path length and the second portions of the first and second lenses have nominally the same second optical path length.

A method for providing a relatively uniform scale image at a detector of a doubly telecentric optical encoder arrangement, the method comprising:

• providing a telecentric imaging configuration including:
• a first portion comprising a first lens located at a first lens plane along an optical axis, a limiting aperture located at an aperture plane along the optical axis, a second lens located at a second lens plane along the optical axis, and a photodetector configuration located at a detector plane along the optical axis,
• a scale grating pattern located at a grating plane along the optical axis, the scale grating pattern extending along a measuring axis direction and having a grating pitch P, and
• an illumination source configured to illuminate the scale grating pattern with a first source light comprising light that is directed parallel to a first plane having a first nominal illumination angle θ relative to a plane that is normal to the measuring axis direction and parallel to the optical axis, and a second source light comprising light that is directed parallel to a second plane having a second nominal illumination angle −θ, the first and second source lights being at least partially coherent and having a wavelength L;
• operating the illumination source to illuminate the scale grating using the first source light directed parallel to the first plane having the first nominal illumination angle θ and the second source light directed parallel to the second plane having the second nominal illumination angle −θ;
• transmitting at least zero order light arising from the first and second source lights at the scale grating to be included in a first scale light;
• transmitting the first scale light through the first lens and toward the aperture plane;
• spatially filtering the transmitted first scale light using the limiting aperture and transmitting that spatially filtered light as first image light;
• transmitting the first image light through the second lens and forming an image of the scale grating pattern on the photodetector configuration;
• and
• providing a displacement signal that is responsive to the position of the image of the scale grating pattern relative to the photodetector configuration along the measuring axis direction,
• wherein:
• the telecentric imaging configuration is configured such that an object point on the scale grating is imaged to a corresponding image point in the image on the photodetector configuration by light included in the first scale light arising at that object point, the first scale light arising at that object point comprising a first symmetric ray bundle including zero order light arising from the first source light and a second symmetric ray bundle including zero order light arising from the first source light;
• the step of spatially filtering the transmitted first scale light using the limiting aperture and transmitting that spatially filtered light as first image light comprises using the limiting aperture to spatially filter the transmitted first scale light and transmit at least a portion of the first and second symmetric ray bundles that include the zero order light arising from the first and second light sources through the limiting aperture to define a pair of imaging ray bundles that contribute to the first image light that reaches the corresponding image point;
• and
• the telecentric imaging configuration is configured such that a first member of the pair of imaging ray bundles passes through a first portion of the first lens and a second portion of the second lens, a second member of the pair of imaging ray bundles passes through a second portion of the first lens and a first portion of the of the second lens, and the first portions of the first and second lenses have nominally the same first optical path length and the second portions of the first and second lenses have nominally the same second optical path length.

A doubly telecentric imaging configuration for use in an optical encoder that senses displacements, the doubly telecentric imaging configuration including:

• a first portion comprising a first lens located at a first lens plane along an optical axis, a limiting aperture located at an aperture plane along the optical axis, a second lens located at a second lens plane along the optical axis, and a photodetector configuration located at a detector plane along the optical axis;
• a scale grating pattern located at a grating plane along the optical axis, the scale grating pattern extending along a measuring axis direction and having a grating pitch P;
• and
• an illumination source configured to illuminate the scale grating pattern with a first source light comprising light that is directed parallel to a first plane having a first nominal illumination angle θ relative to a plane that is normal to the measuring axis direction and parallel to the optical axis, and a second source light comprising light that is directed parallel to a second plane having a second nominal illumination angle −θ, the first and second source lights being at least partially coherent and having a wavelength L,
• wherein,
• the doubly telecentric imaging configuration is configured such that:
• an object point on the scale grating is imaged to a corresponding image point in the image on the photodetector configuration by light included in a first scale light arising at that object point, the first scale light arising at that object point comprising a first symmetric ray bundle including zero order light arising from the first source light, and a second symmetric ray bundle including zero order light arising from the second source light;
• the first scale light is transmitted through the first lens and toward the aperture plane;
• the limiting aperture spatially filters the transmitted first scale light and transmits at least a portion of the first and second symmetric ray bundles that include the zero order light arising from the first and second light sources through the limiting aperture to define a pair of imaging ray bundles that contribute to the first image light that reaches the corresponding image point;
• the first image light is transmitted through the second lens to form an image of the scale grating pattern on the photodetector configuration;
• the photodetector configuration provides a displacement signal that is responsive to the position of the image of the scale grating pattern relative to the photodetector configuration along the measuring axis direction;
• and
• a first member of the pair of imaging ray bundles passes through a first portion of the first lens and a second portion of the second lens, a second member of the pair of imaging ray bundles passes through a second portion of the first lens and a first portion of the of the second lens, and the first portions of the first and second lenses have nominally the same first optical path length and the second portions of the first and second lenses have nominally the same second optical path length.