Cooling apparatus comprises a vacuum chamber, an inner chamber positioned within the vacuum chamber adapted to contain a coolant for cooling target apparatus, and a mechanical refrigerator for refrigerating the coolant and having at least one cooled part in contact with the coolant. The mechanical refrigerator is coupled to one or each of the vacuum chamber and inner chamber through vibration-reducing couplings, so as to reduce the effect upon the target apparatus of vibrations from the mechanical refrigerator.