Business Segments - Business Segments (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Net sales (a):
Net sales	$ 5,458.6	$ 4,614.3	$ 3,086.2
Operating income (loss):
Total operating income (loss)	972.0	624.3	480.1
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	332.2	371.8	116.2
Acquired intangible asset amortization	201.7	149.3	38.8
Capital expenditures (in millions):
Capital expenditures (in millions):	92.6	101.6	71.4
Identifiable assets (in millions):
Assets	14,354.0	14,430.3	5,084.8
Digital Imaging
Net sales (a):
Net sales	3,110.9	2,412.9	986.0
Restructuring Charges:
Restructuring charges		26.4
Digital Imaging | FLIR Systems, Inc
Depreciation and amortization (in millions):
Acquired intangible asset amortization	167.6		110.3
Acquired inventory step-up expense			106.4
Instrumentation
Net sales (a):
Net sales	1,254.0	1,166.9	1,094.5
Aerospace and Defense Electronics
Net sales (a):
Net sales	682.4	628.7	589.4
Engineered Systems
Net sales (a):
Net sales	411.3	405.8	416.3
Operating Segments
Net sales (a):
Net sales	5,458.6	4,614.3	3,086.2
Operating Segments | Digital Imaging
Net sales (a):
Net sales	3,110.9	2,412.9	986.0
Operating income (loss):
Total operating income (loss)	519.3	325.6	192.8
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	279.0	309.2	49.2
Capital expenditures (in millions):
Capital expenditures (in millions):	63.9	64.2	33.4
Identifiable assets (in millions):
Assets	11,432.3	11,756.8	2,000.8
Operating Segments | Instrumentation
Net sales (a):
Net sales	1,254.0	1,166.9	1,094.5
Operating income (loss):
Total operating income (loss)	295.3	253.7	213.2
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	32.6	38.1	38.3
Capital expenditures (in millions):
Capital expenditures (in millions):	9.3	13.3	18.0
Identifiable assets (in millions):
Assets	1,626.4	1,640.3	1,676.2
Operating Segments | Aerospace and Defense Electronics
Net sales (a):
Net sales	682.4	628.7	589.4
Operating income (loss):
Total operating income (loss)	184.1	133.2	80.8
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	12.4	13.2	13.7
Capital expenditures (in millions):
Capital expenditures (in millions):	8.0	8.4	10.4
Identifiable assets (in millions):
Assets	540.1	536.3	567.6
Operating Segments | Engineered Systems
Net sales (a):
Net sales	411.3	405.8	416.3
Operating income (loss):
Total operating income (loss)	39.2	48.6	50.1
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	4.4	7.2	9.2
Capital expenditures (in millions):
Capital expenditures (in millions):	5.3	12.9	7.5
Identifiable assets (in millions):
Assets	200.3	179.2	175.1
Corporate
Operating income (loss):
Total operating income (loss)	(65.9)	(136.8)	(56.8)
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	3.8	4.1	5.8
Capital expenditures (in millions):
Capital expenditures (in millions):	6.1	2.8	2.1
Identifiable assets (in millions):
Assets	554.9	317.7	$ 665.1
Inter-segment eliminations
Operating income (loss):
Total operating income (loss)	$ 25.3	$ 20.2