Summary of Significant Accounting Policies (Narrative) (Details) € in Millions		12 Months Ended
	Jan. 03, 2022	Jan. 02, 2022 USD ($) shares	Jan. 03, 2021 USD ($) shares	Dec. 29, 2019 USD ($) shares	Jan. 02, 2022 EUR (€)
Revenue Recognition
Cumulative catch-up adjustment to revenue		$ 26,800,000	$ 14,600,000
Remaining performance obligation		2,929,000,000
Research and Development [Abstract]
Selling, general and administrative expenses include company-funded research and development		$ 299,300,000	$ 196,000,000	$ 209,600,000
Income Tax Disclosure [Abstract]
Number of years of cumulative operating income used to determine income tax valuation allowance		3 years
Earnings Per Share [Abstract]
Stock options to purchase common stock (in shares) | shares		1,600,000	1,600,000	2,000,000
Cash and Cash Equivalents [Abstract]
Cash and cash equivalents		$ 474,700,000	$ 673,100,000
Cash equivalents held by foreign subsidiaries of Teledyne		294,000,000
Accounts Receivable, Net [Abstract]
Contract liability current		186,000,000	160,100,000
Contract liability noncurrent		25,300,000	14,000,000
Contract asset change		$ 99,900,000
Contract asset change (percentage)		39.60%
Contract liability change		$ 37,200,000
Contract liability change (percentage)		21.40%
Revenue recognized		$ 114,000,000
Reserve for doubtful accounts		13,800,000	12,300,000
Expense of reserve for doubtful accounts		4,500,000	4,100,000	$ 1,300,000
Property, Plant and Equipment, Net [Abstract]
Depreciation		115,200,000	76,600,000	74,500,000
Goodwill and Intangible Asset Impairment [Abstract]
Impairment of goodwill		$ 0	0	0
Deferred Compensation Plan [Abstract]
Deferred compensation employee contribution vesting percentage		1
Deferred compensation liability		$ 115,500,000	68,900,000
Cash surrender value of life insurance		113,400,000	72,600,000
Accrual for Environmental Loss Contingencies Disclosure [Abstract]
Accrual for environmental loss contingencies		6,300,000	6,500,000
Supplemental Cash Flow Information [Abstract]
Cash payments for federal, foreign and state income taxes		83,600,000	74,500,000	110,100,000
Tax refunds received totaled		22,400,000	8,100,000	7,100,000
Cash payments for interest and credit facility fees		117,200,000	19,100,000	23,400,000
Bond financing and debt extinguishment costs		30,500,000
Related Party Transactions [Abstract]
Related party transactions		0	0	$ 0
FLIR
Research and Development [Abstract]
Selling, general and administrative expenses include company-funded research and development		113,800,000
Forward Contracts
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Expected reclassification of loss over the next 12 months		700,000
Currency Swap
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Expected reclassification of loss over the next 12 months		(2,800,000)
Currency Swap Maturing March 2023
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative notional amount		125,000,000			€ 113.0
Currency Swap Maturing October 2024
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative notional amount		150,000,000			€ 135.0
Interest Rate Swap
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative notional amount		125,000,000
Designated as hedging instrument | Buy Canadian Dollars and Sell US Dollars
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative notional amount		148,200,000
Designated as hedging instrument | Buy Great Britain Pounds and Sell US Dollars
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative notional amount		18,900,000
Not designated as hedging instrument
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Loss on derivative instruments		$ 21,900,000
Gain on derivative instruments			$ 7,400,000
Maximum
Goodwill and Intangible Asset Impairment [Abstract]
Threshold period to test goodwill for impairment		3 years
Building | Maximum
Property, Plant and Equipment, Net [Abstract]
Property, plant and equipment, useful life		45 years
Equipment | Minimum
Property, Plant and Equipment, Net [Abstract]
Property, plant and equipment, useful life		5 years
Equipment | Maximum
Property, Plant and Equipment, Net [Abstract]
Property, plant and equipment, useful life		18 years
Computer hardware and software | Minimum
Property, Plant and Equipment, Net [Abstract]
Property, plant and equipment, useful life		3 years
Computer hardware and software | Maximum
Property, Plant and Equipment, Net [Abstract]
Property, plant and equipment, useful life		7 years
Employee stock options
Earnings Per Share [Abstract]
Shares excluded from computation of diluted earnings per share (less than for 2019 and 2018) (in shares) | shares		196,802	239,422	3,000
Restricted stock
Earnings Per Share [Abstract]
Shares excluded from computation of diluted earnings per share (less than for 2019 and 2018) (in shares) | shares		2,608	497	0
Performance shares
Earnings Per Share [Abstract]
Shares excluded from computation of diluted earnings per share (less than for 2019 and 2018) (in shares) | shares		0	0	0
Revenue | Revenue recognized | Recognized at a point in time
Revenue Recognition
Concentration percentage		60.00%
Revenue | Revenue recognized | Recognized at a point in time | Expected
Revenue Recognition
Concentration percentage	70.00%
Revenue | Revenue recognized | Recognized over time
Revenue Recognition
Concentration percentage		40.00%
Revenue | Revenue recognized | Recognized over time | Expected
Revenue Recognition
Concentration percentage	30.00%