Positioning Error Budget Calculator

A translation stage introduces positioning error at the measurement point through four distinct mechanisms. Abbe error arises when the stage pitches or yaws: any angular motion about an axis multiplied by the offset distance between the travel axis and the measurement point produces a linear error (ε = offset × angle). Cosine error occurs when the travel axis is not collinear with the measurement axis; the shortfall is ε = travel × (1 − cos α), where α is the misalignment angle. Thermal error accumulates as the stage body expands or contracts with temperature: ε = CTE × stage length × ΔT. Enter stage angular specifications in µrad or arcseconds, measurement offset, axis misalignment, travel distance, temperature variation, and stage material (aluminum, stainless steel, Invar, or custom CTE) to see individual contributions, RSS total, and worst-case linear sum with a bar chart identifying the dominant source.