System and method of printhead calibration with reduced number of active inkjets

An inkjet printer comprising:

• a printhead including a plurality of inkjets;
• a media transport configured to move a print medium with an image receiving surface in a process direction past the printhead in a print zone;
• an optical sensor configured to detect light reflected from the image receiving surface of the print medium after the print medium moves past the printhead;
• and
• a controller operatively connected to the printhead, media transport, optical sensor, and a memory, the controller being configured to:
• operate the media transport to move the print medium in the process direction past the plurality of inkjets in the printhead;
• operate the printhead to eject a plurality of ink drops from an inkjet in the printhead to form a plurality of marks on the image receiving surface of the print medium, each mark extending in a process direction on the image receiving surface;
• generate with the optical sensor image data of a predetermined portion of the image receiving surface that includes the plurality of marks, the image data including a two-dimensional arrangement of pixels with a plurality of pixel rows extending in a cross-process direction and a plurality of pixel columns extending in the process direction;
• identify a plurality of amplitudes, each amplitude being identified for a portion of each pixel column in the image data of the predetermined portion of the image receiving surface, the portion of each pixel column including expected locations for a portion of the plurality of printed marks in the process direction;
• identify a pixel column corresponding to one of the plurality of identified amplitudes having an absolute value that is a local maximum within the image data for the predetermined portion of the image receiving surface;
• identify a cross-process direction location of the inkjet that ejected the ink drops in the identified pixel column with reference to the identified pixel column;
• store the identified cross-process direction location of the inkjet in the memory for use in printhead registration;
• identify a first sum of a plurality of products formed by multiplication of the image data pixel values in the identified pixel column by a sine function corresponding to the printed pattern of marks in the pixel column;
• identify a second sum of a plurality of products formed by multiplication of the image data pixel values in the identified pixel column multiplied by a cosine function corresponding to the printed pattern of marks in the pixel column;
• identify an offset with reference to an arc tangent of a ratio of the identified first sum divided by the identified second sum;
• identify an average location of the printed marks in the process direction with reference to the offset, a predetermined number of the printed marks, and a predetermined dimension in the process direction for each printed mark in the plurality of printed marks;
• and
• store the average location of the printed marks in the memory for identification of a process direction location of printed ink drops ejected from the inkjet.