Optical-band visibility for touch-sensor mesh designs

A touch sensor that comprises:

• a mesh of conductive material configured to extend across a display, wherein:
• the mesh comprises first lines of conductive material that are substantially parallel to each other and second lines of conductive material that are substantially parallel to each other;
• the first lines extend across the display at a first angle relative to a first axis;
• the second lines extend across the display at a second angle relative to the first axis;
• first lines that are adjacent to each other are separated from each other along the first axis by a first separation distance;
• second lines that are adjacent to each other are separated from each other along the first axis by a second separation distance;
• the first and second angles of the first and second lines and the first and second separation distances of adjacent ones of the first and second lines collectively form optical bands with respect to the display that have an optical-band visibility that is a product of an optical-band contrast function and an optical-band frequency function;
• the optical-band contrast function is
• I
• max
• -
• I
• min
• I
• max
• +
• I
• min
• ,
• wherein Imax is a maximum optical-band intensity and Imin is a minimum optical-band intensity;
• the optical-band frequency function is
• 1
• 1
• +
• (
• f
• /
• K
• )
• n
• ,
• wherein f is an optical-band frequency of the optical bands, K is a constant, and n is a constant;
• and
• the optical-band visibility of the optical bands is less than or equal to 0.11.

A method comprising:

• depositing on a substrate a mesh of conductive material configured to extend across a display, wherein:
• the mesh comprises first lines of conductive material that are substantially parallel to each other and second lines of conductive material that are substantially parallel to each other;
• the first lines extend across the display at a first angle relative to a first axis;
• the second lines extend across the display at a second angle relative to the first axis;
• first lines that are adjacent to each other are separated from each other along the first axis by a first separation distance;
• second lines that are adjacent to each other are separated from each other along the first axis by a second separation distance;
• the first and second angles of the first and second lines and the first and second separation distances of adjacent ones of the first and second lines collectively form optical bands with respect to the display that have an optical-band visibility that is a product of an optical-band contrast function and an optical-band frequency function;
• the optical-band contrast function is
• I
• max
• -
• I
• min
• I
• max
• +
• I
• min
• ,
• wherein Imax is a maximum optical-band intensity and Imin is a minimum optical-band intensity;
• the optical-band frequency function is
• 1
• 1
• +
• (
• f
• /
• K
• )
• n
• ,
• wherein d is an optical-Dana frequency of the optical bands, K is a constant, and n is a constant;
• and
• the optical-band visibility of the optical bands is less than or equal to 0.11;
• and
• forming one or more electrodes of a touch sensor from the mesh of conductive material.