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Fair Value Measurements (Narrative) (Details)
€ in Millions
12 Months Ended
Jan. 03, 2021
USD ($)
Dec. 29, 2019
USD ($)
Dec. 30, 2018
USD ($)
Jan. 01, 2017
USD ($)
Jan. 03, 2021
EUR (€)
Dec. 29, 2019
EUR (€)
Sep. 17, 2019
USD ($)
Sep. 12, 2019
USD ($)
Apr. 11, 2018
USD ($)
Dec. 31, 2017
USD ($)
Jul. 19, 2016
USD ($)
Jul. 19, 2016
EUR (€)
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High $ 7,300,000                      
Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value 2,953,000 $ 35,481,000 $ 69,661,000             $ 65,328,000    
Long-term Debt $ 1,990,649,000                      
Business Combination, Contingent Consideration Arrangements, Maximum Period 2 years 10 months 24 days                      
Business Combination, Contingent Consideration Arrangements, Weighted Average Period 1 year 10 months 24 days                      
Payments for acquisition related contingent consideration $ (10,363,000) (29,942,000) $ (12,800,000)                  
Line of Credit, Maturing September 17, 2024 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Unsecured revolving credit facility, amount             $ 1,000,000,000.0          
Long-term Debt 155,974,000                      
Revolving credit facility outstanding balance 158,600,000                      
Unamortized Debt Issuance Expense 2,600,000                      
Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Long-term Debt, Percentage Bearing Fixed Interest, Amount | €         € 23.1              
Long-term Debt, Percentage Bearing Variable Interest, Amount | €         € 0.1              
Line of Credit, Maturing August 11, 2021 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Long-term Debt   322,000,000.0                    
Revolving credit facility outstanding balance   325,400,000                    
Unamortized Debt Issuance Expense   3,400,000                    
0.6 Percent Senior Unsecured Notes due in April 2021 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Long-term Debt 366,205,000                      
Debt Instrument, Interest Rate, Stated Percentage                 0.60%      
Discount on senior unsecured notes (16,200) (100,000)             $ (200,000)      
Unamortized Debt Issuance Expense   1,100,000                    
3.3 Percent Ten Year Senior Unsecured Notes due in Sept 2029 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Unsecured senior notes, face value               $ 850,000,000.0        
Long-term Debt 840,596,000                      
Debt Instrument, Interest Rate, Stated Percentage               3.30%        
Discount on senior unsecured notes (2,500,000) (2,700,000)           $ (2,800,000)        
Unamortized Debt Issuance Expense 6,900,000 7,400,000                    
Unsecured senior notes, fair value 957,900,000 872,300,000                    
1.875 Percent Ten Year Senior Unsecured Notes [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Long-term Debt 604,715,000 552,200,000                    
Debt Instrument, Interest Rate, Stated Percentage                     1.875% 1.875%
Discount on senior unsecured notes (3,300,000) (3,500,000)                 $ (4,400,000)  
Unamortized Debt Issuance Expense $ 2,800,000 3,300,000                    
Minimum [Member] | Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Debt Instrument, Interest Rate, Stated Percentage 1.10%       1.10%              
Maximum [Member] | Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Debt Instrument, Interest Rate, Stated Percentage 8.90%       8.90%              
Vanadis Diagnostics AB [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Payments to Acquire Businesses, Net of Cash Acquired       $ 32,000,000.0                
Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High       93,000,000.0                
Business Acquisition, Cost of Acquired Entity, Liabilities Incurred, Contingent Consideration at Fair Value       $ (56,900,000)                
Fiscal Year 2019 Other Acquisitions [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Business Acquisition, Cost of Acquired Entity, Liabilities Incurred, Contingent Consideration at Fair Value   634,000                    
Vanadis Diagnostics AB, DNA Labs and Biosense [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Payment for Contingent Consideration Liability, Financing Activities $ 10,400,000                      
Payment for Contingent Consideration Liability, Operating Activities 13,300,000                      
Payments for acquisition related contingent consideration 23,700,000                      
Vanadis Diagnostics AB, SSI and DNA Labs [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Payment for Contingent Consideration Liability, Financing Activities   29,900,000                    
Payment for Contingent Consideration Liability, Operating Activities   20,900,000                    
Payments for acquisition related contingent consideration   50,900,000                    
Euro Member Countries, Euro | Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Other Long-term Debt | €         € 13.9 € 21.3            
Euro Member Countries, Euro | 0.6 Percent Senior Unsecured Notes due in April 2021 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Unsecured senior notes, face value                 $ 300,000,000.0      
Unsecured senior notes, fair value 300,500,000 301,900,000                    
Euro Member Countries, Euro | 1.875 Percent Ten Year Senior Unsecured Notes [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Unsecured senior notes, face value | €                       € 500.0
Unsecured senior notes, fair value 539,800,000 518,500,000                    
United States of America, Dollars | Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Other Long-term Debt | €         17.0 23.8            
Long-term Debt, Percentage Bearing Fixed Interest, Amount | €         € 17.0              
United States of America, Dollars | 0.6 Percent Senior Unsecured Notes due in April 2021 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Unsecured senior notes, fair value 367,100,000 337,400,000                    
United States of America, Dollars | 1.875 Percent Ten Year Senior Unsecured Notes [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Unsecured senior notes, fair value $ 659,300,000 579,600,000                    
United States of America, Dollars | Minimum [Member] | Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Debt Instrument, Interest Rate, Stated Percentage 1.10%       1.10%              
United States of America, Dollars | Maximum [Member] | Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Debt Instrument, Interest Rate, Stated Percentage 4.30%       4.30%              
United States of America, Dollars | Fiscal Year 2019 and 2018 Other Acquisitions [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Business Acquisition, Cost of Acquired Entity, Liabilities Incurred, Contingent Consideration at Fair Value   12,700,000                    
Fair Value, Inputs, Level 2 [Member] | Other Debt Facilities - EUROIMMUN [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Other Long-term Debt | €         € 23.2 € 25.7            
Fair Value, Inputs, Level 2 [Member] | 0.6 Percent Senior Unsecured Notes due in April 2021 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Long-term Debt $ 366,200,000 334,200,000                    
Fair Value, Inputs, Level 2 [Member] | 3.3 Percent Ten Year Senior Unsecured Notes due in Sept 2029 [Member]                        
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]                        
Long-term Debt $ 840,600,000 $ 839,900,000