Methods and apparatuses for automatic restoration detection and automatic restoration of optical communication system are disclosed. The methods and apparatuses disclosed are applicable to a variety of circuits, including but not limited to, sample-and-hold or track-and-hold circuits, quadrature mixers, analog-to-digital converters, digital-to-analog converters, analog or digital filters, and amplifiers. Simultaneously, a timer of the controller 61 is operated to begin counting an incremental time. The capillary separation column can herein be heated uniformly, rapidly and accurately. An initial estimation error is calculated as the difference between the two estimates.