Business Segments - Business Segments (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Net sales (a):
Net sales	$ 5,635.5	$ 5,458.6	$ 4,614.3
Operating income (loss):
Total operating income (loss)	1,034.4	972.0	624.3
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	316.4	332.2	371.8
Acquired intangible asset amortization	196.7	201.7	149.3
Capital expenditures (in millions):
Capital expenditures (in millions):	114.9	92.6	101.6
Identifiable assets (in millions):
Assets	14,527.9	14,354.0	14,430.3
Digital Imaging
Net sales (a):
Net sales	3,144.1	3,110.9	2,412.9
Digital Imaging | FLIR Systems, Inc
Depreciation and amortization (in millions):
Acquired intangible asset amortization	164.0	167.6	110.3
Acquired inventory step-up expense			106.4
Instrumentation
Net sales (a):
Net sales	1,326.2	1,254.0	1,166.9
Aerospace and Defense Electronics
Net sales (a):
Net sales	726.5	682.4	628.7
Engineered Systems
Net sales (a):
Net sales	438.7	411.3	405.8
Operating Segments
Net sales (a):
Net sales	5,635.5	5,458.6	4,614.3
Operating Segments | Digital Imaging
Net sales (a):
Net sales	3,144.1	3,110.9	2,412.9
Operating income (loss):
Total operating income (loss)	517.4	519.3	325.6
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	268.9	279.0	309.2
Capital expenditures (in millions):
Capital expenditures (in millions):	78.2	63.9	64.2
Identifiable assets (in millions):
Assets	11,382.2	11,432.3	11,756.8
Operating Segments | Instrumentation
Net sales (a):
Net sales	1,326.2	1,254.0	1,166.9
Operating income (loss):
Total operating income (loss)	338.3	295.3	253.7
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	27.7	32.6	38.1
Capital expenditures (in millions):
Capital expenditures (in millions):	14.0	9.3	13.3
Identifiable assets (in millions):
Assets	1,692.3	1,626.4	1,640.3
Operating Segments | Aerospace and Defense Electronics
Net sales (a):
Net sales	726.5	682.4	628.7
Operating income (loss):
Total operating income (loss)	199.6	184.1	133.2
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	11.5	12.4	13.2
Capital expenditures (in millions):
Capital expenditures (in millions):	10.9	8.0	8.4
Identifiable assets (in millions):
Assets	569.1	540.1	536.3
Operating Segments | Engineered Systems
Net sales (a):
Net sales	438.7	411.3	405.8
Operating income (loss):
Total operating income (loss)	44.7	39.2	48.6
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	4.4	4.4	7.2
Capital expenditures (in millions):
Capital expenditures (in millions):	3.4	5.3	12.9
Identifiable assets (in millions):
Assets	184.8	200.3	179.2
Corporate
Operating income (loss):
Total operating income (loss)	(65.6)	(65.9)	(136.8)
Depreciation and amortization (in millions):
Depreciation and amortization (in millions):	3.9	3.8	4.1
Capital expenditures (in millions):
Capital expenditures (in millions):	8.4	6.1	2.8
Identifiable assets (in millions):
Assets	699.5	554.9	317.7
Inter-segment eliminations
Operating income (loss):
Total operating income (loss)	$ 29.4	$ 25.3	$ 20.2