Business Segments (Business Segments) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Restructuring Charges:
Restructuring charges	$ 26.4	$ 20.8	$ 3.2
Net sales:
Net sales	4,614.3	3,086.2	3,163.6
Operating income:
Total operating income	624.3	480.1	491.7
Depreciation and amortization:
Depreciation and amortization:	371.8	116.2	111.9
Capital expenditures:
Capital expenditures:	101.6	71.4	88.4
Identifiable assets:
Assets	14,430.3	5,084.8	4,579.8
Digital Imaging
Net sales:
Net sales	2,412.9	986.0	992.9
Instrumentation
Net sales:
Net sales	1,166.9	1,094.5	1,105.1
Aerospace and Defense Electronics
Net sales:
Net sales	628.7	589.4	690.1
Engineered Systems
Net sales:
Net sales	405.8	416.3	375.5
Operating Segments
Net sales:
Net sales	4,614.3	3,086.2	3,163.6
Operating Segments | Digital Imaging
Restructuring Charges:
Restructuring charges	23.9	2.9	1.1
Net sales:
Net sales	2,412.9	986.0	992.9
Operating income:
Total operating income	325.6	192.8	176.5
Depreciation and amortization:
Depreciation and amortization:	309.2	49.2	48.5
Capital expenditures:
Capital expenditures:	64.2	33.4	45.2
Identifiable assets:
Assets	11,756.8	2,000.8	1,874.6
Operating Segments | Instrumentation
Restructuring Charges:
Restructuring charges	1.3	5.9	1.5
Net sales:
Net sales	1,166.9	1,094.5	1,105.1
Operating income:
Total operating income	253.7	213.2	200.4
Depreciation and amortization:
Depreciation and amortization:	38.1	38.3	35.9
Capital expenditures:
Capital expenditures:	13.3	18.0	18.9
Identifiable assets:
Assets	1,640.3	1,676.2	1,680.2
Operating Segments | Aerospace and Defense Electronics
Restructuring Charges:
Restructuring charges	0.7	11.1	0.5
Net sales:
Net sales	628.7	589.4	690.1
Operating income:
Total operating income	133.2	80.8	143.4
Depreciation and amortization:
Depreciation and amortization:	13.2	13.7	14.3
Capital expenditures:
Capital expenditures:	8.4	10.4	19.0
Identifiable assets:
Assets	536.3	567.6	618.3
Operating Segments | Engineered Systems
Restructuring Charges:
Restructuring charges	0.4	0.5	0.1
Net sales:
Net sales	405.8	416.3	375.5
Operating income:
Total operating income	48.6	50.1	36.5
Depreciation and amortization:
Depreciation and amortization:	7.2	9.2	6.0
Capital expenditures:
Capital expenditures:	12.9	7.5	3.6
Identifiable assets:
Assets	179.2	175.1	143.4
Corporate
Restructuring Charges:
Restructuring charges	0.1	0.4	0.0
Operating income:
Total operating income	(136.8)	(56.8)	(65.1)
Depreciation and amortization:
Depreciation and amortization:	4.1	5.8	7.2
Capital expenditures:
Capital expenditures:	2.8	2.1	1.7
Identifiable assets:
Assets	$ 317.7	$ 665.1	$ 263.3