Stockholders’ Equity (Narrative) (Details) $ / shares in Units, $ in Thousands		1 Months Ended	12 Months Ended
	May 14, 2021 shares	Mar. 31, 2021 shares	Jan. 02, 2022 USD ($) installment $ / shares shares	Jan. 03, 2021 USD ($) $ / shares shares	Dec. 29, 2019 USD ($) $ / shares shares	Dec. 30, 2018 shares	Jan. 03, 2016 shares	Jan. 01, 2024 shares	Jan. 01, 2023 installment	Jan. 31, 2016 shares
Preferred Stock
Preferred stock issued (in shares) | shares			0	0	0
Preferred stock, shares outstanding (in shares) | shares			0	0	0
Stock Incentive Plan
Pretax intrinsic value of options exercised			$ 64,200	$ 96,900
Intrinsic value of options outstanding			414,000
Intrinsic value of options exercisable			382,700
Amount of cash received from exercise of stock options			$ 25,400	$ 36,300	$ 34,600
Period used for the exchange traded option included the longest dated options			3 months
Grant date fair value of stock options granted (in USD per share) | $ / shares			$ 134.88	$ 106.26	$ 72.00
Employee stock options
Stock Incentive Plan
Stock options maximum life			10 years
Employee stock options | Year one
Performance Shares and Restricted Stock
Annual award vesting percentage			33.33%
Employee stock options | Year two
Performance Shares and Restricted Stock
Annual award vesting percentage			33.33%
Employee stock options | Year three
Performance Shares and Restricted Stock
Annual award vesting percentage			33.33%
Employee and non-employee stock option
Stock Incentive Plan
Vesting period			3 years
Stock option expense			$ 20,000	$ 24,700	$ 26,100
Nonvested awards unrecognized cost			$ 30,900
Weighted average period for non-vested awards expected to be recognized			1 year 6 months
Performance Shares and Restricted Stock
Share-based compensation expense			$ 20,000	24,700	26,100
Nonvested awards unrecognized cost			$ 30,900
Weighted average period for non-vested awards expected to be recognized			1 year 6 months
Vesting period			3 years
Performance shares
Stock Incentive Plan
Stock option expense				$ 6,200	$ 7,500
Performance Shares and Restricted Stock
Performance period			3 years
Number of equal annual installments | installment			3
Number of shares issued (in shares) | shares			9,588	7,673	8,586	6,481
Share-based compensation expense				$ 6,200	$ 7,500
Performance shares | Subsequent Event
Performance Shares and Restricted Stock
Number of equal annual installments | installment									2
Shares expected to be issued in three installments (in shares) | shares								35,082
Restricted stock
Stock Incentive Plan
Stock option expense			$ 3,500	3,300	3,000
Nonvested awards unrecognized cost			$ 3,500
Weighted average period for non-vested awards expected to be recognized			1 year 6 months
Performance Shares and Restricted Stock
Performance period			3 years
Share-based compensation expense			$ 3,500	$ 3,300	$ 3,000
Nonvested awards unrecognized cost			$ 3,500
Weighted average period for non-vested awards expected to be recognized			1 year 6 months
Restricted stock | Non-Employee Director
Stock Incentive Plan
Grant date fair value of stock options granted (in USD per share) | $ / shares			$ 450.27	$ 312.41	$ 251.23
Restricted stock units (RSUs) | Non-Employee Director
Stock Incentive Plan
Stock option expense			$ 1,200	$ 1,100	$ 1,000
Performance Shares and Restricted Stock
Share-based compensation expense			1,200	1,100	1,000
Fair value restricted stock units granted			$ 130	$ 110	$ 110
Restricted stock units (RSUs) | First Time Director Appointed After Annual Meeting
Stock Incentive Plan
Vesting period			1 year
Performance Shares and Restricted Stock
Vesting period			1 year
Accelerated Share Repurchase Program
Treasury Stock
Number of shares authorized to be repurchased (in shares) | shares			3,000,000							3,000,000
Treasury shares, acquired (in shares) | shares							0
FLIR
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares issued (in shares) | shares	9,500,000
FLIR | Restricted stock units (RSUs)
Stock Incentive Plan
Nonvested awards unrecognized cost			$ 14,400
Weighted average period for non-vested awards expected to be recognized			2 years 2 months 12 days
Performance Shares and Restricted Stock
Nonvested awards unrecognized cost			$ 14,400
Weighted average period for non-vested awards expected to be recognized			2 years 2 months 12 days
Unvested restricted stock units (in shares) | shares		62,974
Restricted stock unit expense			$ 7,800
Outstanding restricted stock units (in shares ) | shares			49,351