Double Exponential Smoothing for Plasma Etching Data

The patent applies preliminary smoothing action before differential processing. By performing smoothing (such as moving average or exponential smoothing) on the raw data before applying finite difference method, the patent eliminates noise that would otherwise be amplified during differentiation. This preliminary preparation of data ensures that subsequent differential operations produce accurate results with high S/N ratio.

The patent introduces smoothing as an intermediary step between raw data acquisition and differential processing. This intermediary smoothing operation acts as a mediator that transforms noisy raw data into smoothed data, which then serves as input for the differential process. The smoothing step mediates the trade-off by reducing noise without requiring complex differential algorithms.

The patent dynamically adjusts the smoothing parameter (such as the number of data points in moving average or the smoothing factor in exponential smoothing) based on the characteristics of the input data. By changing this parameter, the patent can optimize the balance between noise reduction and response time. For rapidly changing signals, a smaller smoothing parameter reduces delay while still providing adequate noise filtering.

The patent employs dynamic smoothing where the smoothing intensity adapts to the signal characteristics. Instead of using a fixed difference interval or fixed smoothing factor, the system adjusts these parameters in real-time based on the observed signal behavior, enabling the system to maintain low delay during rapid changes while achieving high S/N ratio during stable periods.