Business Segments (Disaggregation of Revenue) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Disaggregation of Revenue [Line Items]
Net sales	$ 4,614.3	$ 3,086.2	$ 3,163.6
United States
Disaggregation of Revenue [Line Items]
Net sales	2,932.1	2,078.7	2,179.6
Europe
Disaggregation of Revenue [Line Items]
Net sales	996.1	557.4	565.0
All other
Disaggregation of Revenue [Line Items]
Net sales	686.1	450.1	419.0
United States Government
Disaggregation of Revenue [Line Items]
Net sales	1,193.1	818.2	752.0
Other, Primarily Commercial
Disaggregation of Revenue [Line Items]
Net sales	3,421.2	2,268.0	2,411.6
Digital Imaging
Disaggregation of Revenue [Line Items]
Net sales	2,412.9	986.0	992.9
Digital Imaging | United States
Disaggregation of Revenue [Line Items]
Net sales	1,144.9	309.3	316.1
Digital Imaging | Europe
Disaggregation of Revenue [Line Items]
Net sales	642.7	272.9	299.4
Digital Imaging | All other
Disaggregation of Revenue [Line Items]
Net sales	625.3	403.8	377.4
Digital Imaging | United States Government
Disaggregation of Revenue [Line Items]
Net sales	515.9	120.9	107.4
Digital Imaging | Other, Primarily Commercial
Disaggregation of Revenue [Line Items]
Net sales	1,897.0	865.1	885.5
Instrumentation
Disaggregation of Revenue [Line Items]
Net sales	1,166.9	1,094.5	1,105.1
Instrumentation | United States
Disaggregation of Revenue [Line Items]
Net sales	857.9	844.4	899.7
Instrumentation | Europe
Disaggregation of Revenue [Line Items]
Net sales	248.2	204.4	164.8
Instrumentation | All other
Disaggregation of Revenue [Line Items]
Net sales	60.8	45.7	40.6
Instrumentation | United States Government
Disaggregation of Revenue [Line Items]
Net sales	91.6	80.6	80.4
Instrumentation | Other, Primarily Commercial
Disaggregation of Revenue [Line Items]
Net sales	1,075.3	1,013.9	1,024.7
Aerospace and Defense Electronics
Disaggregation of Revenue [Line Items]
Net sales	628.7	589.4	690.1
Aerospace and Defense Electronics | United States
Disaggregation of Revenue [Line Items]
Net sales	523.5	508.7	588.3
Aerospace and Defense Electronics | Europe
Disaggregation of Revenue [Line Items]
Net sales	105.2	80.1	100.8
Aerospace and Defense Electronics | All other
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.6	1.0
Aerospace and Defense Electronics | United States Government
Disaggregation of Revenue [Line Items]
Net sales	227.2	229.9	225.3
Aerospace and Defense Electronics | Other, Primarily Commercial
Disaggregation of Revenue [Line Items]
Net sales	401.5	359.5	464.8
Engineered Systems
Disaggregation of Revenue [Line Items]
Net sales	405.8	416.3	375.5
Engineered Systems | United States
Disaggregation of Revenue [Line Items]
Net sales	405.8	416.3	375.5
Engineered Systems | Europe
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0	0.0
Engineered Systems | All other
Disaggregation of Revenue [Line Items]
Net sales	0.0	0.0	0.0
Engineered Systems | United States Government
Disaggregation of Revenue [Line Items]
Net sales	358.4	386.8	338.9
Engineered Systems | Other, Primarily Commercial
Disaggregation of Revenue [Line Items]
Net sales	$ 47.4	$ 29.5	$ 36.6