Absolute encoder employing concatenated, multi-bit, interpolated sub-encoders

A position encoder, comprising:

• a scale including spatially periodic first and second tracks, the period of the second track exceeding the period of the first track by a track ratio;
• detector circuitry operative in response to first and second periodic energy patterns from the first and second tracks respectively to generate corresponding first and second sets of analog signals representing respective amplitudes of the first and second periodic energy patterns at predetermined spatial locations;
• and processing circuitry operative in response to the first and second sets of analog signals to:
• (i) generate first and second position sample values of the first and second tracks respectively, each position sample value being an incremental position sample value within a period of the respective track, the second position sample value having sufficient resolution that a predetermined number of least significant digits of the second position sample value are overlapping digits representing nominally the same position information as corresponding most significant digits of the first position sample value, the predetermined number being determined by the magnitude of uncertainty of a spatial phase relationship between the first and second tracks over a predetermined portion thereof;
• (ii) scale the second position sample value by a number corresponding to the track ratio to form a second position estimate value having the overlapping digits occupying the same digit positions as the corresponding most significant digits of the first position sample value,
• (iii) subtract the first position estimate sample value from the second position estimate to create a corrected second position estimate;
• and
• (iv) combine the first position sample value with a non-overlapping most significant part of the corrected second position estimate.