An image measurement apparatus, which functions as a non-contact profile-measuring device, includes: an image sensor as an image pick-up device; a variable focal length lens (liquid lens unit) disposed on an optical axis extending from a workpiece to the image sensor; and a controller (image-pickup lens controller and image measurement processor) configured to control the variable focal length lens and process a detected image by the image sensor. The image measurement apparatus, which also functions as a non-contact displacement-detecting device, includes: an image sensor; a variable focal length lens (liquid lens unit) disposed on an optical axis extending from the workpiece to the image sensor; and a controller (displacement-detection lens controller and profile measurement processor) configured to control the variable focal length lens and a detected image by the image sensor.